THE DESIGN OF 



VALVE GEARS 



FOR 



STEAM ENGINES 



BY 



V^ILLIAM N. BARNARD 

Assistant Professor of Steam Engineering, Sibley College 
Cornell University 



Copyright 1905 by W. N. BARNARD 



ITHACA, N. Y. 
1905 






^I'i 



•X \ 



.■^? 



PREFACE 



Of the many different "diagrams" which are used for investi- 
gating valve motions, nearly all are useful for the purpose of 
analyzing the action of existing gears, but most- of them are 
unsuitable for determining the proportions of new ones. For 
the latter purpose the Bilgram Diagram undoubtedly possesses 
marked advantages over the others. Unfortunately, however, 
it is a little difficult for the beginner to understand and d'oes 
not show how the valve openings vary throughout the cycle as 
clearly as do most of the other diagrams. Usually it should be 
employed for designing only, and then it is often advisable, at 
least for the beginner, to analyze the results obtained by it, by con- 
structing one of the other sirnpler diagrams. For the purpose 
of analysis the Zeuner and the Elliptical Diagrams are generally 
considered to be the best. If one expects to have much to do with 
valve gears, he should have a thorough understanding of these 
three diagrams at least. 

Needing a text-book for his own students, and' finding among 
the many existing works on valve gears, none which employs a 
combination of the Bilgram, Zeuner and Elliptical Diagrams, has 
led the author to attempt to supply the want. 

In preparing this work most of the standard books on the 
subject have been consulted, and much of the text is necessarily 
merely a new treatment of old matter. For that part relating to 
the Bilgram Diagram acknowledgement is due to Mr. F. A. 
Halsey, whose excellent treatise^ "Slide Valve Gears," is the 
exponent of this diagram; arid' to Mr. E. T. Adams, who pub- 
lished some blue print notes on the subject some years ago. 

There is some original matter, and some that has been 
collected' from scattered scources and which has not been embod- 
ied in text-books before. For a great deal of this new matter 
the author is indebted to Professor John H. Barr, formerly 
Professor of Machine Design in Cornell University. Credit for 
matter obtained from other sources is given in the text. 




The treatment is from the graphical standpoint, instead of 
trom the mathematical, and might properly be termed the "Kine- 
matics of Valve Gears." It is assumed that the student is already 
familiar with the action of the simple valve gear with the D-valve, 
and it is intended that the study of the text shall be accom- 
panied by supplementary talks by the instructor and by a drawing 
board course, without which it is practically useless to attempt 
to study the subject. Throughout the text will be found questions 
for mental solution, and problems which require a drawing board 
treatment. Tlie book is so arranged that there is space for the 
student to add notes of his own. 

This opportunity is taken to thank Messrs. R. B. Renner and 
L. Illmer, Jr., for reading parts of the proof and for making 
valuable suggestions. 

Ithaca, N. Y., Aug. 21, 1905. 



CONTENTS 



Part I Simple Slide Valve. 

Part II Multiported and Balanced ValTes. 

Varying Single Eccentric. 

Pai-t in Biding Cutoff Gears. 

Part IV Semirotary and Corliss Gears. 

!Part V Link Gears. 

Part VI Badial Gears. 

Part Vn Poppet Valve Gears. 



Part I 



CHAPTER I. 
THE PLAIN SLIDE VALVE — ^DEFiJNITlONS AND ACTION. 

1. INTRODUCTION. This subject is of such a nature that 
it requires something more than the mere reading and studying of 
text to give one a working knowledge of it. The author believes 
that the only way to master the principles is for each individual 
himself to construct the various diagrams and figures as they are 
explained in the text, (often free hand pencil sketches are sutfl- 
cient for this), and to solve the various problems and to answer 
the questions as he proceeds. 

An extremely valuable asset is the ability to picture in one's 
mind the relative positions of the various parts of .the mechanism 
when the position of one part is known. If the student will make 
a special effort at the outset to develop this ability, and will 
afterwards make constant use of it, he will find that he has a 
great advantage over those who have not taken the trouble to 
acquire it. 

It is assumed that the student is already familiar with the 
arrangement and operation of the simple steam engine having the 
plain slide valve. The purpose of this first chapter is mainly to 
review certain definitions, to bring out certain conceptions, and to 
give the symbols, abbreviations and letters of reference which will 
be used through the text, so as to ensure a common basis of under- 
standing before proceeding with the development of the subject. 

Unless it is stated to the contrary it will be always understood 
that the engine is horizontal with the cylinder to the left, that an 
external D-valve is used and that the crank rotates clockwise. 

2. THE ENGINE. A horizontal engine is said to be running 

over if the crank pin moves away from the cylinder when the 
crank is above the horizontal center line. It runs under when 
the crank is rotating in the reverse direction. In the first 
case the thrust of the connecting rod will cause the cross head to 
always press downward against the lower guiding surface; while 
in the latter case the pressure of the cross head will be upward. 
Engines are usually run over. 

The crank end (C. E.) of the cylinder or valve is the one 
nearest the crank or next to the engine frame. This end is also 
called the front end. The opposite end is the head end (H. E.), 
sometimes called the back end. 

The forward (Fd.) stroke of the piston or valve is that to- 
wards the crank. The return stroke is the baek (Bk.) stroke. 




Fi<&.2L 



Fig. 1 shows a skeleton outline of a simple valve gear having 
a Scotch yoke or slotted crosshead. As the engines are usually 
arranged, the back of the valve, instead of the section or edge» 
would be seen in this view, but for the purposes of analysis it i3 
permissible to consider the valve as turned on its stem to the posi- 
tion shown here. 

Pig. 2 shows the elements of the more usual form of gear, 
that having an eccentric rod. If the eccentric rod is of infinite 
length the motion of the valve will be the same as that which 
would be derived for a slotted crosshead. Such a rod will be 
spoken of as an "infinite rod," to distinguish it from a "finite 
rod," which is of finite length. 

The crank is on dead center when the piston is at the end o£ 
the stroke, and is therefore horizontal on horizontal engines. 
When the piston is at the head end of the cylinder the crank is 
on the head end dead center; when at the other end, the crank is 
on the crank end dead center. 

The eccentric (ecc. or E.) is really a crank pin of such large 
diameter as to surround the shaft. In the discussion of the action 
of the valve gear w^e are only interested in the motion of the center 
of the eccentric, to which the term will be applied hereafter. Be- 
ing a crank, the eccentric has dead center positions. 

The throw of the eccentric is the "eccentricity" or length of 
the crank. (There is a lack of agreement in the use of this term,. 
some using it in the sense given and others as meaning the total 
movement of the valve or "travel.") 



» 



3. THE VATjVE. 




In Fig. 3 is shown a longitudinal section of a valve seat 
and "D-valve," the latter being arranged to admit the steam at 
the ends and to exhaust at its middle. 

The valve seat is the face of the cylinder on which the valvd 
slides. 

The openings in the valve seat for admitting steam to, or 
for exhausting it from, the cylinder are called respectively steani 
and exhaust ports. 

The passages conduct the steam from the ports to the cylin- 
der, or the reverse, and are termed steam or exhaust passages ac- 
cording to their function. 

In engines having' the simple valve the same passages and 
ports are used for both operations. 

The widths of port, of passage and of valve opening are 
measured longitudinally, and the lengths, transversely, with re- 
spect to the cylinder. (In Fig. 3 the port width is p. w.) 

When the simple D-valve is used, the widths, lengths and 
areas of port and passage are usually the same, so the terms 
"port" and "passage" are often considered as being synonymous. 
However, when other types of valves are used the widths (and. 
consequently the areas) are often not the same, and it is then 
necessary to make a distinction in the use of these terms. 

The exhaust cavity, or chamber, or chest, is that space into 
which the exhaust steam flows after leaving the port. 

The bridge is the wall which separates the port from the ex- 
haust cavity. 

The valve is central when it is in the middle of its travel, or 
stroke, the eccentric being vertical either up or down. 

The valve face is that surface of the valve which rests on the 
valve seat. 

The steani and exhaust edges of the valve or of the port are 
respectively those which open to admit steam to, and to exhaust 
it from the cylinder. The outer and iiuier edges of the valve are 
respectively those at the ends and those towara' the middle of th'y 
valve. Similarly, the outer and inner edges of the ports are 



respectively those edges farthest away from and those nearest 
to the center of the valve seat. 

The lap is the distance the edge of the valve is from that edge 
of the port with which it operates and is measured when the valve 
is central. The outside lap (or outer lap) is that of the outer edge 
and the inside lap is the lap of the inner edge of the valve. The 
steam lap (S. L.) and the exhaust lap (Ex. L.) are respectively 
those of the steam and exhaust edges of the valve. The lap is 
positive if the port is closed and negative if it is open. (Negative 
lap is sometimes called "clearance.") In Fig. 3 the exhaust lap 
at the crank end is negative. Similar laps at both ends of the 
valve need not necessarily be the same in amount. 

The valve opening is variable but the term is usually em- 
ployed as referring to the maximum opening. 

When the movement of the valve is more than enough to open 
the port the excess movement is termed the over travel. (O. T. 
in Fig. 3.) 

The width of valve face is the distance between the inner 
and outer edges of the same end of the valve and is therefore 
equal to the sum of the steam and exhaust laps and the port width. 

The valve is said to "take steam from the outside or ends,'* 
and is sometimes termed an "external valve," when the steam en- 
ters the cylinder past the ends and exhausts at the middle, as in 
Fig. 3. Then the outside lap is the steam lap and the inside lap 
is the exhaust lap. 

When a valve "takes steam from the inside or middle," it is 
an "internal valve." Then, the inside lap is the steam lap, and 
the outside is the exhaust lap and the steam and exhaust chambers 
change places. 

The travel or stroke of the valve is the amplitude of its mo- 
tion. 

When there is no rocker arm between the eccentric and the 
valve, arranged to multiply or reduce the motion, the travel of the 
valve is equal to the diameter of the eccentric circle. 

The term displacement, when applied to the valve or piston, 
will be understood to mean the distance the center of the part 
has been moved' from its central position; and in the case of the 
eccentric and crank it will be the horizontal distance from the 
center of the pin to the vertical center line of the shaft. 

If the valve gear having the Scotch yoke (Fig. 1) is used, it 
is evident that the displacements of the valve and of the eccentric 
are equal, and that the valve has simple harmonic motion. If, 
however, the mechanism having an eccentric rod of finite length is 
employed, these displacements will not be equal (except when the 
eccentric is on dead center) and the motion of the valve will not 



be simple harmonic, because of the "angularity" of the eccentric 
rod. The differences between the displacements are usually small, 
however, and when the analysis of the action of the valve is to be 
only approximate, it is often convenient to ignore the inequalities 
altogether and use the displacements given by the Scotch yoke. 
In this case the displacements and positions of the valve will be 
termed' nominal. 

What is true of the valve and eccentric displacements is, of 
course, also true of the displacements of the piston and crank. 

For the present, only the case of the Scotch yoke will be con- 
sidered. The effect of the angularity of the rods will be taken up 
in a later chapter. 

XI. (a) Lay out a symmetrical valve seat, 
with widths of exhaust cavity .5 inches, of bridges 
1 % inches, and of ports 1 ^A inches. 

(b) Draw in its central position an external 
valve having steam and exhaust laps respectively 
1^/4 inches and negative Vs inch for the head end, 
and IVs inches and (positive) % inch for the crank 
end; thickness of metal 1 inch. Dimension and 
label completely. 

(c) If the throw of the eccentric is 2^^ 
inches, what are the overtravels of the steam and 
exhaust edges, and what are the maximum steam 
and exhaust openings, of both ends of the valve. 

X2. Same as XI, but for an internal valve. 

4. THE ACTION OF THE D-VALVE. Looking at Fig. 3, 
it will be seen that, for the steam edge of the valve to be just 
opening, the valve, and consequently the eccentric, must have dis- 
placements equal to the steam lap, in which case the eccentric will 
have rotated past its vertical position, through the angle /I, called 
the lap angle, as shown in Fig. 4 for the head end of the valve. 

When the crank is on dead center, (the piston being at the 
end of the stroke) the steam edge of the valve is usually arranged 
to be open a small amount, which is called the lead. Then the 
valve and eccentric will be dis- 
placed a distance equal to the lap 
plus the lead (Fig. 4), and the 
angle through which the eccentric 
will have rotated past its vertical 
position is called the angle of ad- 
vance, a. The angle through 

Which the eccentric rotates while ^ -?->sK^'^«^'^ ^ FiqA- 
the valve is opening to lead is the 




6 



lead angle, ^ which is equal to [a—A). The exhaust edge 

also has angles of lead and lap, but these terms are always 
understood to apply to the steam edge, unless otherwise stated. 

It is evident that when the throw, lap and lead are known 
the angle of advance is fixed; and that THE ECCENTRIC MUST 
ALWAYS LEAD THE CRANK AT AN ANGLE OF 90 DEGREES 
PLUS THE ANGLE OF ADVANCE (for external valves.) 

Ql. Given, throw 2 inches, steam lap 1 inch, 
and a- 33 deg. Required, (a) amount of lead 
(b) angle of lead, (c) angle of lap, and (d) angle 
between the crank and the eccentric. 

Q2. Given, throw 2%, inches, a 30 deg., 
and lead }i inch and 3-16" respectively at H. E. and 
C. E. Required, the laps. 

Q3. If there is neither lap nor lead, what 
is a equal to and what are the crank positions for 
the opening and closing of the valve? 

The four periods of operation of the valve are admission,, 
expansion, exhaust and compression. 

The four principal valve events are admission (A), cutoff 
(C), release (R) and compression (K). The four minor events 
are maximum displacement of the valve to the right (M), same 
to the left (M') , valve central and moving to the left (Q), and 
central but moving to the right (q). 

The letters given in the parentheses in the above list witlt 
be used to indicate the respective events on the diagrams which 
are to follow. For the principal events of the head end of the 
valve, capital letters will be used; for those of the crank end of 
the valve, small letters will be employed'. 

It will be noticed that each working edge of the valve oper- 
ates two events, opening and closing. The steam edge operates 
both adm. and C. O.; the exhaust edge rel. and comp. These 
pairs of events will be termed conjugate events. 

If the proportions of the different parts of the gear are known 
the action of the valve may be studied by drawing the whole 
mechanism in its different phases. If the valve gear has the 
slotted crosshead the construction may be simplified by consid- 
ering the vertical center line of the cylinder to be moved over to- 
coincide with the vertical center line of the shaft, as in Fig. 5, m 
which case the positions of the centers of the valve and piston 
may be found by simple vertical projection from the centers of 
the eccentric and crank pin, in the manner shown in the figure. 




PiO'5 



Referring to Fig. 5 and considering only the head end of the 
Talve, — when the steam edge is just even with the port edge the 
eccentric, having a displacement S. L., will be at either A or C 
(which are vertically above the center of the valve when it is ia 
this position) ; and when the exhaust edge of the valve is just 
*'line and line" with the edge of the port, the eccentric will be at 
either R or K. Then, considering the direction of rotation, it is 
•evident that when the eccentric is at A the steam edge of the valve 
opens, and when at C this edge closes; at R, the exhaust edge 
opens and at K it closes. The reference letters on the figure, 
therefore, properly indicate the events according to the system 
of notation which has been adopted. 

In a similar manner the position of the eccentric for the 
events of the crank end of the valve may be found. 

If the horizontal diameter of the crank circle is taken to 
represent the stroke of the piston, the position of the latter in 
its stroke may be found by projecting vertically on to that line 
from the crank pin in the manner shown in the figure. In a simi- 
lar way the position of the valve in its travel may be found by 
projecting from the eccentric onto the horizontal diameter of the 
•eccentric circle. 




PERIOP or EXHAUST 



5. After one has become so familiar with the mechanism 
as to be able to form a mental picture of the positions of the valve 
and piston in any phase, the drawing of these may be dispensed 
with; then only the diagram in the upper part of Fig. 5 need be 
constructed. This diagram, which will be called the DIAGRAM 
OF POSITIONS, is shown more complete in Fig. 6, for the head 
end of the valve. 

(a) Referring to Fig. 6, as the eccentric rotates and passe:^ 
the positions which are lettered, the corresponding events or posi- 
tions of the valve are as follows: 



Eccentric at 


Valve Event or Position 


q 


Central, — moving to the right. 


A 


Admission, — just opening to steam. 


I. 


Lead opening. 


M 


Extreme opening to steam. 


C 


Cutoff, — closing to steam. 


Q 


Central, — moving to the left. 


R 


Release, — opening to exhaust. 


M' 


Extreme opening to exhaust. 


K 


Compression — ex:haust closure. 



The positions of the crank pin corresponding to those of the 
eccentric are indicated in Fig. 6 by using the same letters primed, 
with the exception of m and m' which correspond to M and M'. 

(b) In Fig. 6, the line A C, which will be called the Steam 
lap line (for the H. B.), is to the right of YY' a distance equal to 
the steam lap (H. E.). The width of the opening of the valve 
to admit steam is equal to the distance that the eccentric is to 
the right of this steam lap line, as shown by D, when the eccen- 
tric is at B. 



10 



The exhaust lap line R K (for the H. E.) is to the left of YY' 
a distance equal to the positive exhaust lap (H. E.). If the ex- 
haust lap is negative R K will be to the right of YY^ The width 
of opening of the exhaust edge of the valve is equal to the distance 
the eccentric is to the left of the exhaust lap line, 

(c) The effective openings of the steam and exhaust edges 
of the valve are shown by the horizontal sectioning. When the 
exhaust edge overtravels the edge of the port, the maximum effec- 
tive opening is equal to the port width (p. w.). The overtravel is 
O. T. in the figure. 

Note the angles through which both the crank and the eccen- 
tric rotate during each of the four periods. 

The following statements can easily be seen to be true: — 

(d) When the valve is central the crank is at the angle a 
behind the dead center position (either H. E. or C. E., as the case 
may be), i. e. it would have to move through the angle o. in the 
direction of rotation to reach the dead center position. 

(e) When the eccentric is on dead center the crank is at 
-an angle a behind its vertical position (either up or down). 

(f) The valve is moving to the right while the crank rotates 
from m' to m, i. e. while the crank is to the left of the line mm'. 

(g) The valve is displaced to the right while the crank ro- 
tates 180 degrees, starting at a behind the head end dead center, 
i. e. while the crank is above the line Q'q'. It is to the left during 
the rest of the revolution, or while the crank is below Q'q'- 

(h) When the steam edge of the valve is just beginning to 
•open the crank is at an angle ^ (lead angle) behind the dead 
center position (either H. E. or C. E. as the case may be). 

(i) The valve has the same position (displacement) for 
both the opening and the closing of any one of its edges; but the 
directions of motion are, of course, opposite. 

(j) When the opening of the valve occurs after it, or the 
eccentric passes the central position, the lap is positive; when 
the reverse is true the lap is negative. 

(k) Fig. 7 shows the ideal indicator card corresponding to 
Fig. 6. 

Diagrams similar to Fig. 6 and 7 can be constructed for the 
crank end of the valve in like manner. When the laps at both 
ends of the valve are equal, the eccentric and crank positions for 
the C. B. are diametrically opposite those for the head end of the 
Tralve. 



11 



X3 Construct a Diagram of Positions for a 
valve having the dimensions given in XI, the angle 
of advance being 32 i/^ deg. ; (a) for the H. E.; (b) 
for the C. E. 

X4. Construct a Diagram of Positions for 
a valve having zero laps and no lead; (a) for the 
H. E.; (b) for the C. E. 

X5. Given d) equals 5 deg., a equals 30 deg., 
throw 2 inches, crank radius 3 inches, angle for re- 
lease 10 deg. Required, both laps, the lead, and 
the crank and piston positions for all events. 

Q4. Considering each of the four valve events 
in turn, will they be made to occur earlier or later 
(a) by increasing the laps; (b) by decreasing them; 
(c) by increasing a; (d) by decreasing a ? 

Q5. Are the conjugate events both affected 
similarly (a) by changing the lap; (b) by changing « ? 

Q6. (a) Where will the valve be when the 
crank is at the angle a behind each of the four 
"quarter-positions" (0 deg., 90 deg., 180 deg., 
270 deg.)? 

(b) Wheie will the crank be at the time of 
admission? 

Q7. (a) If the outer edge of the valve opens 
when the crank is 33 deg. behind the dead center 
and a is 30 deg., is the lap positive or negative? 

(b) Same but with a equal to 36 deg. 

(c) Same as (a) but for the inner edge. 

(d) . .Same as (b) but for the inner edge. 



CHAPTER U. 

THE ELEMENTARY VALVE DIAGRAMS. 

6. VALVE DIAGRAMS. These should show by simple and 
accurate geometrical constructions the action of all parts of a 
valve gear throughout the complete cycle of operation. These dia- 
grams are sometimes used for the purpose of analyzing the action 
of valve gears the proportions of which are already known; and 
at other times for designing, that is, to determine the proportions 
of valves to give certain predetermined steam distributions with 
certain widths of openings. There are a number of different con- 
structions used' for valve diagrams, some of which are better for 
analysis, and others better for designing. Often it is desirable to 
use a combination of two or more diagrams for a thorough inves- 
tigation, as certain features are shown more clearly by some dia- 
grams than by others. 

The elements of the more common diagrams will be briefly 
discussed in this chapter. We will consider only tliat mechan- 
ism which has the slotted crosshead both at the eccentric and at 
the crank pin. 

As none of the valve diagrams show the true positions of the 
eccentric, it is frequently advisable to show these by drawing lit- 
tle figures opposite the crank pin in its various positions, as is done 
in several of the illustrations which follow. These little figures 
will be called Pilot Diagrams. 

Each of the diagrams which will be discussed should be 
applied to the solution of the first of the following typical prob- 
lems and an attempt be made to solve the second. In this way the 
possibilities and limitations of the various diagrams will become 
apparent. 

These diagrams should be drawn full size, with the excep- 
tion of the crank pin circle, which may be made any size what- 
ever as we are only interested in the crank angles and in the 
piston position expressed as a fraction or as per cent of stroke. 
Often the eccentric circle is used for the crank pin circle. If a 
circle 6*^ inches in diameter in used then each 1-16 inch is 1 
per cent of the stroke. 



13 



'^^ X6. Analysis. Given the throw 3 inches, 

angle of advance 31^^ deg., both steam laps 1% 
inches, positive exhaust lap for crank end of the 
valve V2 inch, negative exhaust lap for head end 
% inch and widths of both ports ll^ inches. Re- 

"' quired for both ends of the valve, — 

(a) The crank and piston positions for all the 
■^ events; 

I (b) The angles of rotation of crank and ec- 

? Cintric for each of the periods; 

(c) The maximum openings to steam and 
exhaust; 

(d) The overtravel (steam and exhaust) ; 

(e) The lead. 

i 

X7. Design. — Given cutoff % stroke, (A) the 
amount of lead V^ inch or (B) the lead angle 5 
deg., the maximum width of opening of the steam 
edge of the valve 1^/4 inch, release 95 per cent of 
stroke for H. E. and 90 per cent, for C. E. Deter- 
mine for both ends the value of (a) the angle of 
' advance, (b) throw, (c) steam lap, (d) exhaust lap, 

(e) crank and piston positions for each event and. 

(f) the overt^avpi of hnth the steam and exhaust 
«dges. 



14 



COMSTRUCTION 




Diagram 

7. THE SINUSOIDAL DIAGRA3I. The harmonic motious 
'of the valves and piston can be shown by using rectangular co- 
ordinates, plotting the displacements as ordinates on the crank 
positions as abscissae. The resulting curves are sinuoids. In Pig. 
8 the crank angles are measured from the H. E. dead center, the 
positive ordinates are for displacements to the right, and the 
negative ones are for displacements to the left. 

The method of constructing a sinusoid is shown in the upper 
Tight hand corner of the figure. The valve sinusoid crosses the 
X-axis when the crank angles are (180 degrees minus a), and (360 
degrees minus a) , and its ordinates are maximum when the 
angles are (90 degrees minus a), and (270 degrees minus a), since 
these are the respective angles for zero and maximum displace- 
ments of the valve. 

It will be remembered that, when the displacement is equal 
to the lap, the valve is either just closing or just opening and 
that any greater displacement is equal to the width of opening. 
If, then, "lap lines" are drawn parallel to the X-axis and at dis- 
tances from it equal to the laps, the intersections of these lines 
vrith the valve sinusoids will determine the crank angles for vari- 
icus events, and the portions of the ordinates beyond these lines 
will represent the valve openings. In the figure the steam and 
exhaust lap lines are AC and RK for the H.E.; and ac and rk 
for the C. E. The periods of opening for the head end are shown 
by the areas which are section lined. The maximum effective 
opening of the exhaust edge is equal to the port width (p. w.). 
The overtravel is O. T. The lead openings occur, of course, when 
Jthe crank angle is deg. and 180 deg. 



15 



This diagram requires considerable time and care to con- 
struct, especially when accuracy is essential. It is useful for 
analyzing the action of a valve gear of which proportions art 
already known, as in X6, but can not be used for the solution ot 
design problems like X7. 

8. THE ZEUNER DIAGRAM. If, using the polar co-ordin- 
ates, we lay off the valve displacements (regardless of the sign) 
as radii-vectores on the corresponding positions of the eccentric 
arm, as in Fig. 9, the locus of the points plotted will be the two 
circles with centers at o and q/ and' having diameters equal in 
the throw of the eccentric. These loci will be called displacenient 
circles, and in the figure that for displacements to the right is 
shown by the bold line and that for displacements to the left by 
fine line. When the eccentric is at E the displacement of the 
valve is D, and it is to the left. 



**DK- 




FielO 



If the valve displacements are laid off radially along the cor- 
responding crank positions (instead of on the eccentric positions 
as in Fig. 9), we have the Zeuner diagram which is shown in Fig\ 
10. In this figure, as before, the displacement circle which is 
shown by the bold line is for the displacements of the valve to 
the right. When the crank is in the position OP the displace- 
ment of the valve is equal to D, and is to the right. 

The axis O B of the "displacement circles" is at the angle 
a behind the Y-axis, for this is the position of the crank when 
the valve has the greatest displacement. The valve is central 
when the crank is in either of the positions OA or OA', at right 
angles to the axis OB. 



IG 



In applying this diagram it is often convenient to let the 
eccentric circle also represent the crank circle, as is done in Fig. 
11. In this figure the positions of the crank pin for the valye 
events are shown by the usual reference letters with primes. The 
lap lines are evideudy arcs of circles with radii equal to the laps, 
those shown in the figure by the bold lines AC and RK being 
respectively the steam and exhaust laps for the head end, and 
those shown by the fine lines ac and rk being the laps for the 




crank end. The effective openings (shown by the radial section 
lines) and the crank positions for the different events are shown 
for the head only, those for the crank end being admitted to 
avoid complicating the diagrem. The lead opening occurs, of 
course, when the crank is on dead center, the amount and angle 
of lead for the H. E. being shown in the figure. It will be seen 
that the chords A' C and R' K' are tangent respectively to the 
steam and exhaust lap arcs. 

This diagram is simple to understand, easy to construct, and 
shows at a glance the action of the valve throughout the whole 
cycle. The true eccentric positions are not shown and when the 
laps are small (and those for the exhaust usually are) the crank 
angles and piston positions for the valve events can not be deter- 
mined very accurately. 

This diagram is very useful for analyzing the action of a 
valve gear when the proportions, including the throw of the 
eccentric, are known (as in Problem X6). It can also be used to 
design a valve to meet a given set of conditions (as in Problem 
X7), but, especially when the throw of the eccentric is not given-, 
this involves rather complicated constructions, which will be omit- 
ted as there is another diagram which is much better to use for 
this purpose. 



17 




9. SWEET DIAGRAM. In Fig. 12, a' C and R' K' are 

respectively the steam and exhaust lap lines for the H. E. trans^. 
ferred from the Diagram of Positions, Fig. 6. Letting the eccen- 
tric circle also represent the crank circle, then, when the eccentric 
is in positions A' knd C the corresponding positions of the 
crank pin will be A and C. In the Sweet diagrams the chord 
AC is the steam lap line (H. B.). Similarly when the eccentric 
pin are R and K and the exhaust lap line (H. E.) is the chord 
RK. The axis Oy is parallel to the lap lines. 

It is evident that if the axis OY and the lap lines of the 
Diagram of Positions are rotated back through the angle 90 deg. 
plus a, they will coincide with the similar lines on this new 
diagram. In the former diagram the lap lines 'are chords between 
eccentric positions, in this latter one they are chords between cor- 
responding crank pin positions (taken on the eccentric circle). 

It will be evident that the lap lines are at a distance from O 
equal to their respective laps; that they and the axis Oy are 
inclined at an angle a with respect to the ^L^orizontal axis; that 
corresponding to any crank position, the displacement of the 
valve is equal to the perpendicular distance from the crank pin 
to the axis Oy, (as shown by D when the crank is at OP) ; that, 
similarly, the opening of the valve is equal to the perpendicular 
distance from the crank pin to the lap line; and that the lead, 
which is the opening when the crank is on the dead center, is 
equal to the radius of a circle which is tangent to the steam lai) 
line and has center at X (for H. E.). 

In the figure the effective openings of the valve (shown by 
the section lines) and the positions of the crank pin for the vari- 
ous events are shown for the head end of the valve only, ac and 
rk are the lap lines for the crank end. 



18 



In the Zuener Diagram, Fig 11, compare the chords A'C and 
R'K' with the lap lines on the Sweet Diagram. 

This Sweet Diagram gives accurate results, is easy to under- 
stand can be applied readily to problems of analysis (Prob. X6) 
but problems of design (Prob. X7) can be solved only by using 
more or less complicated constructions, which we need not con- 
sider. This diagram is also known as the Reuleaux Diagram. 




10. ELLIPTICAL DIAGRAM. To show at a glance the 
simultaneous displacements of the valve and piston throughout 
the complete revolution of the engine, the displacements of the 
valve may be plotted as ordinates on the corrosponding positions 
of the piston as abscissae. The resulting figure will be an ellipse 
as is shown in Pig. 13. To have the generating point move around 
the ellipse in the direction in which the crank rotates (as shown 
by the arrows), the displacements of the valve to the right are 
plotted as positive ordinates (up), and those to the left as nega- 
tive ordinates (down): 

In this diagram the lap lines are AC and RK, for the head 
end of the valve. The effective openings to steam and exhaust, 
the points for the various events and the lead are shown in 
the usual manner for the H. E. For the crank end of the valve 
the same ellipse would be used but the laps would, of course, be 
laid off opposite to those for the H.E., as shown by the fine lines 
ac and rk. 

In constructing this diagram the displacements of the valve 
and of the piston can be obtained from any of the other diagrams, 
including the Bilgram which is to follow, but most readily from 
the Zeuner. 

This diagram can not be used for the solution of problems 
in design such at Problem X7, but is of the greatest value for 
analyzing (Prob. X6) as it shows at a glance the operation of the 
valve throughout the whole cycle. 



11> 

11. THE BILGRAM DIAGRAM. The diagrams which have 
already been discussed were seen to have their limitations. All 
can be used for analyzing; some are applicable to problems In 
design only by employing rather complicated constructions, ana 
others not at all; some give accurate results and others do not. 

The Bilgram Diagram, which will be considered next, is un- 
limited in its application, is simple to construct and always gives 
accurate results. It is especially valuable for designing and is the 
diagram which we will use most frequently for that purpose here- 
after. Unfortunately it is a little harder to understand and does 
not show the action of the valve throughout the complete cycle 
quite as clearly as do the Zeuner and Elliptical Diagrams, so these 
latter and other diagrams will be used to supplement it at times. 
Like all of the other diagrams, the Bilgram does not show the 
true positions of the eccentric, since it uses only the crank posi- 
tions. 

(a) In the Bilgram Diagram for the H. E. the angle of 
advance is laid off above OX' (Fig. 14) 
locating on the eccentric circle the point 
Q, which is called the lap circle center. Q 
is a stationary point and must not be con- 
fused with the eccentric center. 

Before showing the manner in which 
this point is used it is necessary to fix in 
mind certain of the relative movements 
and positions of the crank and valve. 

In this figure, MM' is at right angles 

to Qq and consequently each of the points Q, q, M and M^ is at the 
angle a behind the nearest axis. 

Noting the positions of the crank an^ eccentric in the little 
Pilot Diagrams the following statements (b, c, d and e) will be 
seen to be true. 

(b) The valve is central when the crank coincides with 
either OQ or Oq. The valve is moving to the left when the crank 
is at OQ, and to the right when at Oq. 

(c) The valve is displaced to the right while the crank 
rotates from Oq to OQ, i. e. while the crank is above Qq. The dis- 
placement is to the left when the crank is below Qq. 

(d) The maximum displacement to the right occurs when 
the crank is at OM. That to the left occurs when the crank is 
at OM . The valve will have its maximum opening or closure 

when the crank is in one or the other of these positions, depend- 
•ing on which of the edges of the valve is under consideration. 




"20 ■ • 

(e) The valve is moving to the right while the crank is 
rotating from OM'' to OM i. e. while the crank is to the left of 

JVIM'. The motion is to the left when the crank is to right of MM' 

(e') Considering the head end of the valve and referring 
to Fig. 6, it is evident that: — 

The steam edge closes when the crank is near OQ. 
The steam edge opens when the crank is near Oq. 
The exhaust edge closes when the crank is near Oq. 
The exhaust edge opens when the crank is near OQ. 

Q8. When the valve is moving to the left and 
is approaching its central position, where will the 
crank be? "When moving to the right and' ap- 
proaching the central position, where will the crank 
be? Devise other questions of similar nature. 

(f) Now, considering the use of the point Q: — In Fig. 15, 
when the crank OP is On the H. E. dead center the eccentric is 
at E at the angle a with OY. Now if the crank rotates through 
any angle /? to OP' the eccentric will of course rotate through the 
■same angle to E^ The eccentric will then be at the angle a plus 
,/? with OY and will have a displacement equal to E'D'. From Q 

draw the line QD perpendicular to 
the crank OP (produced if neces- 
sary). Then it can be seen that 
the right triangles OQD and O E'D' 
are equal. It follows that QD and 

FloiS "' '^'^ E'D' are equal, since they are 

homologous sides of equal trian- 
gles. This is evidently true for all positions of the crank. But 
^D is the perpendicular from Q to the crank and E'D' is the 
displacement of the valve. Therefore, CORRESPONDING TO 
ANY POSITION OF THE CRANK, THE DISPLACEMENT OF 
THE VAIiVE IS EQUAL TO THE LENGTH OF THE PERPEN- 
DICULAR DROPPED FROM THE FIXED POINT Q TO THAT 
ORANK POSITION (produced if necessary). This is the FUNDA- 
MENTAL PRINCIPLE OF THE BILGRAM DIAGRAM. To get 
the displacement of the valve corresponding to a given crank 
position, it is only necessary to measure the perpendicular distance 
from the fixed point Q to the crank. The position of the eccen- 
tric need not be found. If one constantly remembers this Funda- 
mental Principle and will picture in his mind the positions and 
motion of the valve corresponding to the various positions of the 
«rank (as explained in b, c, d and e) there will be little difficulty 




21 

in using the Bilgram Diagram. If one has difficulty in forming 
these mental pictures, he should draw the little Pilot Diagrams 
opposite the crank in its different positions. 

(g) T*iere will be considerable use for the term "perpen- 
dicular" in connection with the application of this diagram, so to 
avoid the necessity of explaining the manner in which the term is 
employed each tim«, it will always be understood to refer to the 
perpendicular from Q to the crank and may mean either the per- 
pendicular direction or the length of the perpendicular, as the 
•context will indicate. 




(h) The locus of D the foot of the perpendicular is evi- 
dently a circle with OQ as diameter, (why?) as is shown in Pig. 
16 for the head end of the valve. 

(i) By subtracting the lap, QL (same fig.) from the valve 
displacement QD, the width of valve opening LD is found. Since 
the lap is constant, a "lap circle" may be drawn with Q as center 
and with radius equal to the lap, then the valve openings are 
the portions of the perpendiculars outside of this circle, (as shown 
by the shaded area in the figure). 

(j) The width of valve opening is zero when either crank 
itself, or its extension, is tangent to the lap circle; one position 
of the crank being for the opening of the valve, and the other 
for the closing, depending on which way the valve is moving and 
^hich edge is operating. The foot of the perpendicular and 
point of tangency coincide when the crank is in either of these 
positions. 

(k) The closing of the outer edge of the valve occurs when 
the crank itself is tangent to the lap circle, (no matter on which 
side). For, considering the head end of the valve, when the 



22 



outer edge is closing the crank will be near Q (see e') and con- 
sequently the crank itself will be tangent. 

(1) The closing of the inner edge of the valve occurs when, 
the extension of the crank is tangent to the lap circle. The open- 
ing of this edge of the valve occurs when the crank is tangent to 
the lap circle on the side opposite that to which it is tangent for 
closing. 

X8. On X3 draw the steam and exhaust lap 
circles for a Bilgram Diagram and see if the crank 
positions are as stated above. 
(m) The lap is positive if the closing occurs when' the point 
of tangency is on the "back side" of the lap circle, for the 
closure will then take place before the crank reaches Q, i.e, 
before the valve has reached its central position. 

(n) The lap is negative if the closing occurs when the point 
of tangency is on the forward side of the lap circle. When the 
lap is negative use broken lines for the lap circle. 

Q9. Considering the H. E. of a D-valve, (a) 
what are the directions of displacement and of mo- 
tion when the steam edge with positive lap is just 
opening? (b) Then on which side of the lap circle 
will the tangency be, and will the crank or its 
extension be tangent to the circle? Devise similar 
questions for the other edge for both opening and 
closing and both positive and negative laps. An- 
swer by reasoning and not by lapplying rules. 
(o) The lead opening of the valve is equal to the shortest 
distance from the lap circle to the X-axis, since this is the opening 
when the crank is on the dead center. A line drawn parallel to 
OX' and at a distance equal to the lead opening above it, will bet 
tangent to the lap circle. 

(p) The maximum opening of the valve is equal to OR 
(Fig. 16). Then if with O as center and w'ith radius equal to 
the maximum width of valve opening, an arc is struck, it will be 
tangent to the lap circle at B. The maximum closure is equal 
to OF. 

Fig. 16 is for the H. E. outer edge of the valve, the lap being. 
positive. The valve is open when the crank rotates from A to C 
and is closed during the remainder of the revolution. It is evi- 
dent that OQ bisects the angle between OC and the extension ot 
OA. 

(q) In a Bilgram Diagram for the crank end of the valve 
the lap circles would be drawn with centers at q, diametrically 
opposite Q, and all the preceeding statements are still applicable. 



23 




Fiil7 ' Fie 15 

(r) Complete Bilgram Diagrams are shown in Fig. 17 for 
the head end of a valve and in Fig. 18 for the crank end. Th© 
angle of advance and throw of the eccentric must be the same 
in both these diagrams since they refer to the same eccentric, 
"but the laps of the two ends of the valve are not the same. The 
exhaust lap for the crank end is negative and is therefore shown 
T3y a dotted circle. These two diagrams could be combined into 
one, but are shown separated here to avoid confusion. 

(s) The application of the Bilgram Diagram to problems 'n 
analysis, like X6, is very simple. After the eccentric circle has 
been drawn, the lap circle center Q is located and the lap circles 
for steam and exhaust edges are drawn. The crank positions for 
the various events are tangent to the I'ap circles. 

(t) The application to design problems when the cutoff, 
lead opening and maximum valve opening to steam are known, is 
as follows: — In Fig. 19 for the H. E. of the valve, starting with 

the X and Y axes, draw the crank 
position OC for cutoff; draw a line 
parallel to OX and above at a dis- 
tance equal to the lead; and with O as 
center and radius equal to the desired 
maximum valve opening strike an arc 
in the position shown. From what 
has gone before it is evident that the 
steam lap circle must be tangent to 
these three lines. The location of its 
center Q can usually be found as 
quickly and as accurately by trial, as by geometrical construction. 
Having the point Q determined, the throw and angle of advance 
of the eccentric and the lap are known. 

If, in Fig. 16, instead of the lead opening, the lead angle (p 
IS known, Q will be so located that the lap circle will be tangent 
to OC, to OA produced and to the arc for width of valve opening. 




24 



If now, the crank position OK for compression is drawt.. 
(Fig. 19), the exhaust lap circle will of course have its center at 
Q and will be tangent to this line produced. The crank position 
for release will be tangent to this same circle on the other side. 

12. PSEUDO-POIjAR DIAGRAMS is the term which will be 
used as referring to the Zeuner, the Sweet, and the Bilgram. 
Diagrams. 



CHAPTER III. 

ARRANGEMENTS AND LL>nTATIONS OF THE SEVIPIiE VALVE; 
GEAR. ANGULARITY OF RODS AND EQUALIZA- 
TION OF VALVE EVENTS. 



ARRANGEMENTS OF THE SIMPLE VALVE GEAR. 

13. "RUNNING UNDER" or backward rotation. Applying, 
the general rule for external valves, that 
the eccentric must lead the crank at an an- 
gle of 90 deg. plus a , the position of the 
eccentric with respect to the crank for back 
ward rotation is that shown in Fig. 20. 

QIO. In turning the eccentric 

to reverse an engine what will be 

the angle between the new keyway 

and the old? 



\ *}^^ 



F16.20 



It is evident that the valve diagrams would be reversed, 
with respect to the horizontal center line, from those for engines, 
which "run over," as is shown in the lower part of the figure for 
the Bilgram, Zeuner and Elliptical Diagrams. 

X9. Same as X6 but for engine running 
under. 

14. INTERNAL VALVES. Since the motion and displace 
ments of the internal valve must be just opposite from those ot 
the external valve, the eccentric must be 
diametrically opposite that for the latter 
case and therefore will follow the crank at 
an angle of 90 deg. minus a , as in Fig. 21. 

Qll. Where will the eccentric 
be when an internal valve is used on 
an engine which runs under? 
To avoid confusion, in constructing the valve diagrams for 
internal valves it is advisable to ignore the fact that the valve is; 
in internal, and draw the diagrams the same as for external valvos. 

15. VALVE ROD GUIDES. It is usually advisable to guide 
the end of the valve rod in some manner and this may be done- 
by using either a sliding guide (crosshead), or a rocker arm. If 
the rocker arm is used the pin moves in a circular arc, and cons*?-^ 
quently has movement sidewise as well as longitudinally. (See- 




26 



V/alveRoo p j£C.Roo 



— T 



/ 
/ 



Pig. 22). It is necessary to make pro- 
vision for this lateral movement of the 
•end of valve rod and this may be done 
either by using a rod which has con- 
siderable flexibility or by introducing in 
the rod some form of "knuckle joint." 
The arc should be so located' that the 
lateral movement of the pin is the same 
in amount on either side of the center 

line of the rod. Of course the longer the arm of the rocker, the 
less will be this side movement. 

When the end of the eccertric rod is joined to the end of 
the valve rod in such a manner that the valve and eccentric nom- 
inally have the same amounts and directions of displacement, the 
arrangement will be called a '^direct drive." 

If the guiding rocker is pivotted half way between the pins 
tor the eccentric rod and valve stem, as in Fig. 
2 3, the motion of the valve is of course re- 
versed from that derived from a direct drive, 
so either the eccentric must be placed diamet- 
rically opposite that for the latter case or else 
an internal valve must be used. This ar- 
rangement having the reversing rocker may 
"be conveniently used when the center lines 
of the valve rod and eccentric rod are some 
•distance apart. 

Q12. On an engine which runs under and has 
an internal valve and reversing rocker, where 
would the eccentric be placed? 

Sometimes the rockers are arranged to give the valve either 
a greater or a smaller movement than 
that derived directly from the eccentric. 
These are termed multiplying or reduc- 
ing rockers as the case may be and are 
■shown in Pig. 24. 

16. In constructing the valve dia- 
•grams when this last type of rocker is' 
employed, it is convenient to use an im- 
aginary, or^Virtual" Eccentric, which is 
of such size that it would cause the 
^alve to have the same motion if a 
direct drive were used. The diameter 
of the virtual eccentric circle is there- 
iore equal to the travel of the valve. 




FieZd 



fv»o 



VALVg, - BJaC'. 

\/(cg \/(b) 




' "^w^tce- Roc 

R6X¥ 



The diagrams will show the true values for the laps, the open- 
ings of the valve, and the angle of advance, and will give the true 
angular positions of eccentric and crank; but the throw is, ol 
■course, not that of the actual eccentric. A drawing showing the 
true arrangement of the linkage should accompany the valve 
diagram. 

Q13. What is the radius of the virtual ec- 
centric when a multiplying rocker having a ratio 
of arms 3 to 2, is used with an eccentric of throw 
equal to 2 inches? 



>WD/ETFVWtl^ 







FigSS 



17. DISTORTION OF VALVE MOTION BY ROCKER ARM. 

The travel of the valve is of course equal to the perpendicular 
projection of the arc of the rocker pin onto the center line of 
the valve stem, and the valve is central with its seat when the 
pin is in the middle of its arc. In Fig. 25, in which the arc is 
oblique to the center line of the valve stem, 
the valve is central when the pin is at P. It 
is seen that, with this arrangement of rocker, 
the motions of the valve to either side of its 
central positions are not the same, as shown 
by the difference between a and b. In order 
that these motions shall be equal, it is evi- 
dent that the rocker arm must be at right an- 
gles to the valve stem when the valve is cen- 
to the valve stem when the valve is central. 

It will also be apparent that the rocker arm must at the same 
time bear the same relationship to the eccentric rod. To cover 
the case of rockers having separate arms for the pins of the valvfa 
rod and eccentric rod, the general statement may be made that 
the center lines of the arms of the rocker must be at right angles 
to their respective rods when the valve is central, to avoid distor- 
ing the valve motion. 

If the eccentric and valve rods are not 
parallel a bent rocker arm or bell crank 
must be used, as in Fig. 2 6 b, to satisfy the 
Tule just given. 

Q14. What is the relation be- 
tween the angle between the rocker 
arms and that between the rods? 

Q15. Sketch several arrange- 
ments of both the direct and reversing types, tak- 
ing the rods at different angles. 



fVw 




28 




Fibzr 



18. POSITION OF ECCENTRIC WITH OBLIQUE ECCEN- 
TRIC ROD. Referring to Fig. 27, when the valve is central the 
rocker arm will be in the position FHG, and the eccentric will 
be nominally at ^' at right angles to the line OF, which is the 
mean or "nominal" position of the eccentric rod. When the 
crank is on the dead center P, the eccentric must evidently be 
advanced the angle a ahead of this position E)', and will con- 
sequently be at E. No matter what sort of guide is used for tbe 
end of the eccentric rod it is evident that the general rule for tlie 
position of the eccentric is as follows for external valves: — When 
the crank is on the H. E. dead center the eccentric will be (90 
deg. plus a ) ahead of the nominal position of the eccentric rod. 
Only when the eccentric rod is parallel with the center line of the 
engine will the eccentric be (90 deg. plus a) "ahead of the crank," 
as the rule is usually stated. Fig. 2 7 is for an internal valve. 

Q16. What is the angle between the crank 
and the eccentric when the eccentric rod is inclined 
upward at 30 deg. and the angle of advance is 30 
deg. (a) for external valve with reversing rocker, 
(b) for external valve with direct drive, (c) and 
(d) same as (a) and (b) but for internal valve. 

Q17. On an engine having tw^o cylinders and 
two cranks at 90 deg. how may the same eccentric 
be used to drive both valve gears? (b) Same, when 
the angle between the cranks is 130 deg. 



29 



ANGULARITY OF THE CONNECTING ROD. 

19. DISTORTION DUE TO ANGULARITY. In Pig. 28, 
o is the middle of the stroke and the distance oO is equal to the 




FTe-25 



length of the rod aP. If an infinite rod is used, the displacement 
of the piston oa will of course be equal to the displacement of the 
pin P which is equal to OA. If, however, a finite rod is used 
these displacements will not be equal. For, if the end of the rod 
a is kept stationary and the other end P is uncoupled and swung 
to A', then oa will be equal tc OA', which is seen to be greatei 
that OA. It will be found that no matter where the crank Is; 
A' will always be to the right of A. It is evident that owing to 
the angularity of the connecting rod, if one of finite length is 
used, the piston is always nearer the crank end of the strol.e 
than it would be nominally, except of course when it is at the 
end of its stroke. 

It follows that: — The valve events occur later in the Up- 
ward stroke and earlier in the return stroke than they wouldl 
nominally. 

The distance AA' is the "distortion due to the angularity oi 
the rod" and is equal to the difference between the length of the^ 
rod and its horizontal projection. This distortion is greatest 
when the crank is at right angles to the center line of the engire 
and decreases to zero at the ends of the stroke. The shorter tha. 
length of the rod when compared to the crank radius, the 
greater is this relative distortion. 

If the diameter of the crank circle XX' represents the stroke 
of the piston, then, having any position, such as A', the corres- 
ponding position of the crank pin P may of course be found by 
drawing the "connecting rod arc" A'P; or if P is known at the 
start, A' may be found from it in a similar manner. 

The way the distortion varies throughout the stroke is shown 
by Fig. 29, which may be called a Diagram of Distortions. Plot- 



30 




Actum. n»moNS. 



tins nominal piston positions as ordinates 
and true piston positions as absciassae gives 
the curve ADC. When the piston has trav- 
eled nominally half the stroke, if the move- 
r"'ent is from the H. E., it has actually tra- 
versed the distance ED; and if the piston 
is in the return stroke, its distance from 
the crank end is FD, which is much less, 
than ED. The scale for the forward stroke 

is at the bottom of the diagram and that for the back stroke is at 
the top. 

If, now, the nominal displacements are plotted as abscissae 
on the same ordinates as before the straight line ABD is of course 
obtained. Then the horizontal distances between this line and 
the curve ADC are the distortions. When the piston has trav- 
eled nominally half stroke the distortion is BD. If the movement 
is from the H. E. the piston will be this distance beyond half 
stroke and if from C. E. it will be the same distance short of 
mid-travel. It is evident that the difference between the actual 
distances traveled from the two ends of the stroke is twice the 
distortion, and that the mean between these distances is the 
nominal distance traveled. 

On "high speed'* engines the length of the connecting rod 
is usually six times the crank radius; on "low speed" engines 
It is often 5^^ cranks; and on marine engines it is sometimes 
even as short as 4 cranks. 

XIO. Draw a Diagram or Distortions to any 
suitable scale, the length of the connecting rod be- 
ing six times the crank radius. Tabulate the per 
cent, difference between the events at the two ends 
of the valve, the events occurring nominally as 
follows: — CO. % stroke, release .90; comp. .85. 
Same for connecting rod lengths equal to 5, 5 Vz 
and 6 V2 cranks. 



20. VALVE DIAGRAMS CONSIDERING "ANGULARITY." 

All the pseudo-polar valve diagrams show the true positions of 
the crank. Therefore if the positions of the piston are not being 
considered, but only those of the crank, the angularity of the 
connecting rod would not affect the diagram. If, however, after 
the crank positions have been found, the true positions of the 
piston are desired, it will then be necessary to consider the angu- 



31 



larity. Having already determined the crank positions, the cor- 
responding true position of the piston would be found by drawing 
the connecting rod arcs in the manner shown in Fig. 30a and b 
for the Bilgram and Zeuner Diagrams. Should the piston posi- 
tions be known at the outset, then by drawing similar arcs, the 
true crank positions can be found and these would be used in 
constructing the rest of the diagram. 




rie.30 



In the Elliptical Diagram, Fig. 30c, it is evident that the 
angularity causes all points on the ellipse to be displaced to- 
wards the crank end of the stroke. The resulting figure is of 
oval shape, in consequence of which the diagram is sometimes 
called the Oval Diagram. The Sinusoidal diagram is distorted in 
a similar manner. 

Xll. In X6 find the true positions of the pis- 
ton for each of the events on each of the diagrams, 
when the connecting rod is six times as long as the 
crank. 

X12. Using the data of X7 construct a Bil- 
gram diagram considering the angularity of the 
connecting rod of* "length equal to six cranks." 

21. THE ^rULLER CIRCLES. In Fig. 31, O is the center 
of the shaft, o P' is the crank, a' P' is the connecting rod, OA 13. 
the frame, AB the stroke, 6 
the angle between the crank 
and the frame, and a' A is the' 
distance the piston is trom the 
head end of the stroke. When 
the crank pin is at P, on the 
dead center, the end of the 
connecting rod coincides with 
A. Keeping the crank station- 
ary in the position OP and ro- 
tating the rest of the mechan- 
ism about it, the frame will 
turn about O, the points A and 
B describing the circles 3 and 




1, and the connecting rod will 



rotate about P, its end describing the circle 2. 1, 2 and 3 are 
the Muller Circles. 

When the frame has rotated through the angle 6 to the 
position O A' the end of the connecting rod is at a on circle 2, 
and A' a, which is equal to A a\ is the distance the piston is from 
the head end of the stroke, properly corrected for the angularity 
of the connecting rod. Since O A' coincides with O P' produced, it 
is evident that, when the frame is in its normal position OA, to 
find the true location of the piston in its stroke it is only neces- 
sary to prolong the crank to intersect the Muller Circles. 

These Muller Circles may be drawn concentric with any ot 
the pseudo-polar valve diagrams. 

X13. Around the diagram XI 2 draw the Mul- 
ler circles and compare the piston displacements 
obtained therefrom for the different valve events 
with those used in constructing the diagram. 

EQUALIZATION OF VALVE EVENTS. 

When a finite connecting rod is used with a valve having 
the same amount of lap at both ends, the displacements of 
the piston for similar events in the two strokes are unequal, 
or, as it is usually stated, the valve events are unequal. The 
expedients which may be employed with more of less success to 
equalize the events are, (1) to use unequal laps, (2) to dis- 
tort the valve motion by using an oblique guide for the end of 
the eccentric rod', and (3) to use a combination of (1) and (2). 

22. EQUALIZATION BY USING UNEQUAL LAPS. In the 
Bilgram Diagram in Fig. 32, in which Q and q are respectively 
the centers of the head and crank 
end lap circles, let it be desired 
to have the exhaust edge of the 
valve close when the piston is at 
k' in the forward stroke and 
at K' on the return, these points 
being at equal distances from 
their respective ends of the 
stroke. Striking the connecting 
rod arcs in the usual manner, the 
corresponding true crank posi- 
tiops Ok and OK are found. For 
the compression to begin when 
the crank is in either of these positions, the back side of the 
proper lap circle must be drawn tangent to the extension of 
the crank, as is shown in the figure by the bold lines. The lap 
circles for the two ends of the valve will be unequal, that for 
the head end being the smaller (when positive). Using these 




33 



unequal laps, this one valve-event will be equalized. But each 
of these edges of the valve operates another event (opening or 
release) which occurs when the crank itself is tangent to the 
lap circle on its front side, the crank being at OR and Or. It 
will be found that this event will not be equalized by using these 
lap circles but that the inequality will be less than that which 
occurs when the laps are equal. 

For the sake of comparison the "nominal" lap circles (which 
are a mean between those just found for the two ends of the 
valve), together with the corresponding true positions of the 
crank and piston, are shown in fine lines in this same figure. 

In the foregoing case the nominal lap was assumed to be 
quite large. 

In the special case when there is zero nominal lap, as in tbs 
Bilgram Diagram shown in Fig. 
33, K' and k' are the perpendicu- 
lar projections of Q and q on the 
horizontal axis, and the correction 
will give a small negative lap cir- 
cle at Q (H. E.) and a (practic- 
ally) equal positive circle at q 
(C. E.). Then, the crank position 
for closure at one end will (prac- 
tically) coincide with its position 
for opening at the other end, i. e. 
K falls on r and k on R. There- 
fore, since the closure has been 
equalized, the opening will also be. 

In the foregoing cases only the exhaust lap has been con- 
sidered, and for this it is seen that the head end lap is the 
smaller, algebraically. If the steam events are equalized the 
crank end lap will be the smaller. 

It is seen that, in general by making the laps unequal one 
event may be exactly equalized, and the inequality in the conju- 
gate event be reduced; and that in case the nominal lap is zero, 
the exact equalization of both events is possible. 

It is usually considered to be more important to equalize 
lead and compression than cutoff and release. For equal leads 
the steam laps will be equal. 

X14. Throw 2 inches, a= 33 deg., compres- 
sion 85 per cent, of stroke. Construct a Bilgram 
Diagram, (a) for the nominal exhaust laps; (b) for 
exhaust laps giving equalized compression; (c) 
tabulate the true piston positions, in per cent, of 




34 



stroke, for both compression and release, for both 
(a) and (b). 

X15. Same as the preceding exercise, but for 
the case of zero nominal laps. 
23. EQUALIZATION BY USING OBLIQUE GUIDE. It is 
assumed that the valve diagram has been constructed (neglecting 
the angularity of the rods) to determine the angle of advance 
and the throw of the eccentric. 

In Fig. 34, which is a diagram showing the true positions of 
the various parts of the valve gear, the larger circle is for the 
crank pin, and the smaller one is for the eccentric. On the 
diameter of the crank circle, locate the positions of the piston, 
in both strokes, for equal cutoffs and equal admissions and note 
that these events are conjugate. By drawing the connecting rod 
arcs from these positions of the piston, find A', C, a' and c', the 
true positions of the crank pin for these events. The corres- 
ponding positions of the eccentric. A, C, a and c, are determined 
next. Now with A and C as centers and with radius equal to the 
length of the eccentric rod, strike arcs intersecting at B; and in 











a similar manner, with a and c as centers get the intersect- 
ing arcs D. Remembering that the valve, and consequently 
the .guide for the eccentric rod, will occupy the same position 
for both the opening and closing of any one of the edges, 
it is evident that if the end of the eccentric rod is guided 
so as to pass through the points B and D, this pair of conjugate 
events will be equalized. In the figure an oblique rocker arm 
FEf, pivoted at E, is employed as a guide, the eccentric rod 
being attached to pin F and the valve rod to f. The pivot E 
might have been placed above the axis instead of below it, or a 



3& 



crosshead with an oblique guide could be substituted for the 
rocker. 

The rocker arm should be so designed that, when the ec- 
centric rod pin is at P, half way between B and D, the other arm 
of the rocker Ef, will be at right angles to the valve rod. Then 
the laps at the two ends of the valve will be equal; but they will 
usually be slightly different in amount from that found by the 
valve diagram. If b, f and d are the positions of the valve rod. 
pin corresponding to B, F and D, the amount of lap at the head 
and crank ends of the valve will be the horizontal distances be- 
tween b and f and between d and f, respectively. 

The extreme positions of the rocker pin for the eccentric, 
rod may be found by striking arcs with O as center and with 
radius, first, equal to the sum of the length of the eccentric rod 
and the throw of the eccentric, and then, equal to their difference. 
It will be found that the maximum openings of the two ends of 
the valve will be unequal and different from those which were- 
used in the valve diagrams; but these differences are usually so 
slight as to be of no consequence. However, there may be- 
exceptions to this last statement, and in such cases it will be- 
necessary to increase the throw of the eccentric, or to lengthen 
the rocker arm Ef. If this latter is done, the eccentric rod will 
be oblique with the center line of the engine, and the angle 
between the crank and eccentric will be changed to correspond. 

In Fig. 34a, the end of the eccentric rod is guided by a 
crosshead sliding obliquely along BD, and the valve rod is joined 
by the link VB to the same pin to which the eccentric rod is. 
attached. Neglecting the angularity of the link VB, which is 
shown abnormally short in the figure, it is evident that the hori- 
zontal distance between B and D is the sum of steam laps of the 
two ends of the valve, and that if these laps are equal the valve 
will be central when the crosshead pin is at F half way between 
D and B. The laps and maximum openings are shown in the. 
figure. 

Instead of an oblique crosshead a simple rocker arm could 
be similarly employed. 

Usually only one pair of conjugate events can be equalized by 
this method, for, if besides the intersecting arcs for admission and 
cutoff, others for release and com- 
pression, are drawn, there would 
then be four points, B, D, H and I, 
in Fig. 3 5, through which to pass ^ 
the arc of the rocker pin and this ^^^ 
is usually an impossible construc- 
tion. It is generally considered to ^ W — tT X-Jr^ 
be more important to equalize Ad- * • I600- 
mission and Cutoff than release and compression. 




36 



The equalization of both release and compression, in addi- 
tion to admission and cutoff, may be sometimes approximatod 
closely enough by making the arc of the rocker pin come as near 
to passing through the intersections H and I (Fig. 35) as is 
possible, "splitting the difference." 

In the special case when the nominal lap is zero, the exact 
■equalization of both exhaust events, in addition to admission and 
cutoff, is possible, for then the intersections H and I will coincide 
and there will be only three points for the arc to pass througli. 
X16. (a) Construct a nominal Bilgram Dia- 
gram for a valve to have Vs inch lead, C. O. % 
stroke, compression 90 per cent, throw 2 inches. 
Find the angle of advance and the crank and piston 
positions (nominal) for admission. 

(b) With a length of connecting rod equal to 
six cranks and using an eccentric rod 15 inches 
long, equalize admission and cutoff, and approxi- 
mate the equalization of the exhaust events, by 
using a rocker similar to that shown in Fig. 34. 
Take EF 10 inches long. 

If the opening of the valve at either end is too 
small, the arm Ef may be lengthened, but at the 
same time it must be made perpendicular to an 
oblique center line passing through O. This new 
line is then the new center line of the engine, and 
while it is oblique on the paper it is horizontal on 
the engine. The angle between this line and the 
horizontal is the inclination of the eccentric rod on 
the engine and the position of the ecc. with respect 
to the crank must be changed to correspond. In- 
stead of lengthening the arm Ef, the throw may 
be increased. What are the dimensions of the 
steam and exhaust laps and openings? 

X17. Same as preceeding but using a cross- 
head guide instead of a rocker. 
24. OBLIQUE GUIDE AND UNEQUAL LAPS. Having 
equalized the steam events, one of the exhaust events (preferably 
compression) may be equalized by making the exhaust laps un- 
equal. Having located the positions of the eccentric for .the 
equalized compression, from these points as centers and with 
radius equal to the length of the eccentric rod, arcs are struck 
intersecting the arc BD, in Fig. 35, at J and K. The correspond- 
ing positions of the valve rod pin are j and k, and the exhaust 
laps will be the horizontal distances between f and j and between 
1 and k. Release will of course not be equalized. 



37 



X18. In the two preceeding problems find 
the exhaust laps for equalized compression and then 
find the crank and piston positions for release. 

ANGULARITY OF THE ECCENTRIC ROD. 

25. DISTORTIONS DUE TO ANGULARITY. Just as the 
angularity of the connecting rod affected the positions of the 
piston, so also the angularity of the eccentric rod affects the 
positions of the valve, causing it to be always nearer the crank 
end of the stroke than it would be nominally. This of course 
affects the valve events, making some to occur later and others 
■earlier. 

In the Diagram of Positions shown in Fig. 36, when a Scotch 
yoke is used in the valve gear, the H. E, and C. B. steam lap lines 
are respectively AC and ac, and the corresponding leads are the 
distances ED and ed. Now, em- 
ploying an eccentric rod in place 
•of the yoke, if, when the steam 
edge of the H. E. of the valve is 
■even with the edge of the port, 
the rod is uncoupled at the eccen- 
tric and that end is swung across 
the shaft, it will draw the "steam 
lap arc" A' B C^ The distance the 
eccentric is to the right of this 
arc is the steam opening for the 
H. E. The steam lap arc for the 
'C. B. is a' b c' and the distance the 
eccentric is to the left of this line 
is the steam opening for that end. 
It is seen that the lead opening EF for the H. E. is greater than 
ED by the amount FD; that for the crank end the opening ef is 
less than ed by the same amount; and that the events, instead of 
•occurring when the crank pin is in the positions A, C, a and c, 
will occur when it is at A', C, a' and c'. 

26. CORRECTING FOR ANGULARITY OF ECCENTRIC 
ROD. Now, it is seen that if either the valve rod or the eccen- 
tric rod is lengthened an amount equal to FD, the steam lap arcs 
will be shifted so as to pass through D and d, respectively, thus 
completely correcting the leads and changing the steam laps to 
be equal to OB' and Ob^ Further, the cutoff will be very nearly 
corrected, as will also be the exhaust events, for the exhaust 
lap arcs R' K' and r' k' will be moved over to very nearly pass 

through the points R and K and r and k. When the valve is 
<;entral on its seat, the end of the rod would trace the arc Hh, 




38 



which crosses the Y-axis at points G and g, which coincide witti 
the horizontal projections of E and e onto that axis. 

In Fig. 36 the eccentric rod was purposely taken abnormally 
short, to cause the distortions to be exaggerated. The longer the 
rod is, the smaller will be the distortions and with the usual 
lengths they are so small that the designer may safely neglect, 
them altogether and construct the diagrams the same as for the 
case • of the valve gear having the Scotch yoke. Then, when 
the valves are "set" in the shop, either the eccentric rod or the 
valve rod, which are usually adjustable, may be lengthened suffi- 
ciently to correct the leads. 

X19. On the diagram of X3 show the correc- 
tion for equalized lead when the eccentric rod is 30 
inches long. 

27. THE VALVE DIAGRAMS CONSIDERING ANGULAR- 
ITY. In case the eccentric rod is unusually short, or for some^ 
other reason, it is desired to draw diagrams showing the effect 
of the angularity of the eccentric rod, the constructions of the 
various diagrams must be modified. In the Diagrams of Posi- 
tions it has been seen that the lap lines are eccentric rod arcs. 
Since the Sweet Diagram is really this former diagram rotated 
back through the angle 90 degrees plus a, it also would have arcs, 
for steam lap lines. 

In the Zeuner Diagram the displacement curves will no 
longer be circles but will be oval figures, that for displacements, 
to the right being broader, and the one for those to the left 
being narrower than the circles. These displacement curves may 
be obtained by plotting as radii vectors the true valve displace- 
ments on the corresponding crank angles. 

In the Bilgram Diagram, the fundamental principle is not. 
applicable to this case, so the diagram can not be used. 

In discussions hereafter the effect of the angularity of the- 
eccentric rod will be ignored. 

X20. On the diagrams X6 show the correc- 
tion for the angularity of an eccentric rod which is 
20 inches long. 



28. LIMITATIONS OF THE SIMPLE VALVE. It is im- 
practicable to have cutoff occur much before % stroke, because, 
in order to obtain a satisfactory width of opening with earli'?! 
■cutoff, it is found (1) that the valve and eccentric are excessively 
large, (2) that consequently the valve gear must work against 
great friction and inertia forces, and (3) that the release and 
•compression occur too early in the stroke. 

X21. Construct a nominal Bilgram Diagram 
for a valve which is to cutoff at y^ stroke, have 1 
inch maximum opening to steam, and ^ inch lead, 
(a) What are the throw and angle of advance? (b) 
With release at 90 per cent, of stroke, where will 
compression begin? 



CHAPTER IV. 

FACTORS USED IN DESIGNING — AREAS OF PASSAGES, DIS- 
TRIBUTION OF STEAM, DRAWING THE VAXiVE, ETC. 



In this chapter the discussion will not be limited to the case 
of engines having the simple D-valve, but will be extended in 
some instances to include also those types which are still to be 
considered. The matter relating to these latter cases may be^ 
omitted until the study of them is taken up later. 

29. SPEED AND VELOCITY. These terms are often used 
ambiguously. When the "speed of the engine" is spoken of, the 
rotative speed of the crank is meant and this is usually expressed 
in revolutions per minute. By piston speed" (V) or velocity, the 
mean velocity of the piston is generally meant. This is usually 
expressed in ft. per minute, and is equal to twice the stroke (L), in 
feet, multiplied by the r. p. m. (N), i. e. V=2IvN. The same 
term may also be applied to the instantaneous velocity of the 
piston when in some particular position in its stroke. Similarly, 
the term velocity of steam may mean either the mean or the 
instantaneous value, but usually the former. The context gen- 
erally indicates in what sense the terms are used, if they are 
employed loosely. 



30. COMMERdAIi TYPES OF STATIONARY ENGINES. 

It is unnecessary here to discuss the different types or arrange- 
ments of engines except possibly to explain very briefly what is. 
meant by the terms "high," "medium" and "low speed engines" 
as applied to the better grades of commercial types, as thesfr 
terms will be used later. By "speed," when used in this connee-^ 
tion, is meant the rotative speed. Of course for a given "piston, 
speed" the greater the stroke is, the smaller will be this rotative- 
speed. 

HIGH SPEED ENGINES are those which have high rotative 
speeds accompanied by strokes which are very short when com- 
pared to the diameter of the cylinder, the piston speed being gen- 
erally in the neighborhood of 600 ft. per minute. The stroke is. 



4i 

usually about equal to the diameter of the cylinder, sometimes 
more and sometimes less. These engines almost always have a 
single, balanced valve and a shaft governor. They are often 
called "short stroke engines," and are designed to occupy the 
smallest space, have the least weight, and "direct connect" to 
the smallest dynamo for a given power, of any of the stationary 
commercial types. This class includes only engines of compar- 
atively small power, the cylinders being not usually made larger 
than 20 inches in diameter. 

LOW SPEED ENGINES are those having long strokes (from 
2 to 4 times the diameter of the cylinder) and usually operate 
at less than 120 r. p. m., the speed being limited by the valve- 
gear, the action of which becomes unreliable at higher speeds. 
This class includes engines having the Corliss and other types 
of trip cutoff gear. The governor is usually of the "fly-ball' 
type. The piston speed depends on the r. p. m, and the stroke. 

MEDIUM SPEED ENGINES have rotative speeds and strokes 
intermediate between the foregoing. Positively driven multiple 
valves are generally used and the cutoff is often operated by a 
separate valve. The governor is nearly always of the "shaft 
type." The piston speed is around 600 feet per minute, being 
higher on the larger engines. 

The medium and low speed engines are usually of larger 
power than the high speed. 

There is no sharp dividing line between these different types, 
of engines and it is sometimes difficult to decide in which class an 
engine belongs. 

31. AREAS OF VALVE OPENINGS. Of course, from one 
standpoint, the larger the openings the better will be the results; 
obtained, for the less will be the throttling, or "wire-drawing" of 
the steam. But with larger openings there will be greater 
weight and cost of parts, increased clearance volume, and greater 
frictional and inertia forces of the valve gear, which latter not only 
decrease the mechanical eflSciency of the engine but also disturb 
the action of the shaft governor, if one is used. Therefore the 
problem before the designer is to determine how small it is 
advisable to make the openings. 

For the rate at which the steam is supplied to the cylinder 
to be always equal to the rate at which the volume is displaced 
by the piston, the following expression must be satisfied: — 



42 



in which 



"Then 



av = AV 

a = area of passage fsq. in., usually) 
A = " " piston (same unit) 

V = velocity of steam (ft. min., usually) 

V = " '* piston (same unit j 

V = AV -^ a 
a = AV ^ V 



(1) 



(2) 
(3) 




5team 
VEiActnes 

(C) 






Applying equations 1, 2 and 3 to the 
How of steam through the opening of the 
valve, A is the only constant quantity in 
them. How the other quantities, a, v and 
V, vary, will now be shown, the valve 
opening considered being that of the steam 
edge of the head end. 

Assuming that the piston has simple 
harmonic motion, it will be remembered 
that for such motion, if the velocity of the 
-crank pin is represented to some scale by 
OP, the radius of the crank pin circle. Fig. 
37a, then the ordinate of the crank pin Px 
represents the velocity of the piston to the 
same scale. Under these conditions the 
Curve of Piston Velocities is a circle, the 
ordinates being the velocities and the abs- 
cissae the positions of the piston. If any 
other scale is used for the ordinates, the 
curve becomes an ellipse. If the cutoff 
takes place when the piston is at C, the 
ordinates during the period of admission are those under the 
arc XPc. 

A Diagram of Valve Openings is shown in Fig. 37b for the 
steam edge of the valve, the ordinates being areas of openings, 
and the abscissae the piston positions as before. This diagram 
is really that part of the Elliptical Diagram (see Fig. 13) which 
lies above the steam lap line, the scale being changed to read 
areas instetid of widths of openings. 

Now since we know A, the area of the piston, and have 
•curves giving simultaneous values of a and V, then from equation 
(2) the various values of v may be computed. If these are plot- 
ted as ordinates on piston positions as abscissae, the Curve of 
Steam Velocities, Fig. 37c, is obtained. 







43 

It is seen that the steam velocity is comparatively small in 
the early part of the stroke, but rises to infinity when the valve 
closes, the curve becoming assymptotic to the ordinate at C. 

Now, when the opening becomes very restricted, ard the 
velocity of fluid is very great, the throttling, or "wire-drawing,'" 
will prevent a nonexpansive fluid, such as water, from following 
up the piston and therefore the pressure in the cylinder will fall 
off. The velocity at which this failure of the working fluid takes 
place will be termed the critical velocity and is shown by the 
ordinate v^ in Fig. 37c, the piston being at K. In the case of 
an expansive fluid, however, such as steam, after this point i& 
reached the fluid which is already in the cylinder, and the little 
which still manages to enter, expands to fill the space behind 
the piston so the pressure drops much more gradually than in 
the former case. 

liy comparing the indicator cards taken from the cylinder 
with those taken simultaneously from the steam chest, as in Fig. 
37d, we may determine K, the position the piston occupies at 
the time when the admission line begins to round off towards 
cutoff. Then computing the velocity of the steam through *^he 
effective opening of the valve, corresponding to this piston posi- 
tion, the critical velocity is determined. From data obtained in 
ths way from several engines of different types the critical velocity 
of steam was found to be about 14,000 feet per minute, by Pro- 
fessor M. E. Gutermuth, of the Technical High School of Darm- 
stadt.* 

Each kind of valve has its typical curve of steam velociti^^s, 
and those which cause K to be nearer to C (Fig. 37c) of course 
give the sharper cutoffs. In the case of the simple slide valve, 
the maximum opening of the valve will be considerably more, 
and the corresponding velocity of the steam, proportionately less 
than the critical. 

32. VALVE OPENINGS USED IN DESIG^^NG. The Gu- 
tennuth Method of determining the proper valve openings is as 
follows: — First having selected the point on the indicator carl 
where the rounding towards cutoff is to begin, note the position 
of the piston and determine its velocity. Then using equation 3, 
compute the area of the critical opening, for v equal to H,'JOO It. 
per minute or less. The valve gear can now be designed to give 
this opening when the piston is in the position previously selected, 
and to give openings corresponding to velocities less than the 
critical, before this point is reached. 



*See Journal Am. Soc. Naval Engineers, May 1904. 



44 



The usual method followed in the past has been to entirely 
disregard the critical opening, and design the valve to have a 
maximum opening which corresponds to a velocity of steam which 
has been found by experience to give satisfactory results. The 
maximum area of opening is found by using equation (3) ; but V is 
the mean velocity of the piston (2LN), and v is the "mean vel- 
ocity of the steam." In practive v varies from 6,000 to 10.000 
feet per minute, but it is usually in the neighborhood of 8,000 

The shorter and more direct the passages, and the more 
rapid the opening and closing of the valve, the higher may be 
the velocity allowed. When it is desired to have an especially 
sharp cutoff, the valve is given wider opening (corresponding 
to a low velocity), fhe edge sometimes even overtraveling the 
back edge of the port. This is of course at the expense of hav- 
ing to use somewhat larger parts in the valve gear. 

As the steam lap is always a great deal larger than the 
exhaust lap, on a D-valve, the opening of steam is much more 
restricted' than that to exhaust. In designing the gear it is only 
necessary to see that the steam opening is sufficiently large, for 
the exhaust opening will always be more than is required. 

The width of the valve opening is of course equal to the area 
divided by the length, which is nearly always equal to that of 
the port. 

33. AREAS OF PORTS AND PASSAGES. The area of 
the piston and that of the passage are constant qualities, so, if 
the passage were always open, the velocity of the steam through 
it would be directly proportional to the velocity of the piston. 

In determining the area of a passage, equation (3) is used, 
but it is customary to use for V the mean velocity of i)iston and 
for V a "mean velocity of steam" which has been found by 
experience to give satisfactory results. 

In 1895, under the direction of Professor John H. Barr, data 
relating to the proportions of engine parts was obtained from a 
large number of manufacturers of standard commercial types of 
stationary engines.* This collection of material covered nearly 
two hundred simple engines of sizes ranging from 20 to 750 horse- 
power. From these data the mean velocities of steam through 
the passages were computed. In the following table are given 
the results, including the range of velocities found and the values 
which appeared to be the mean practice, the latter being in bold 
type: — 

*" Current Practice in EJngine Proportions" by J. H. Barr, Trans. A. S. M. E., 
Vol. XVIII, 1897. 



4J> 



MEAN VELOCITY OF STEAM IN FEET-MINUTE. (BARR) . 



Type of Engine 


High Speed 


Corliss 


Steam pipe 


5800-6500-7000 


5000-6000-8000 


Exhaust pipe 


2500-4400—5500 


2800—3800—4700 


Exhaust passage 


4500—5500—6500 


4000—5500—7000 


Steam passage 


(Same passage) 


5000-6800—9000 



It is seen that the values used in practice vary over a wide 
range. 

It will be remembered that on "single valve" engines, whicli 
class includes nearly all the high speed engines, the same pn Vi- 
sage is used for both admitting steam to and exhausting it from 
the cylinder, and therefore must be made large enough for the 
latter function. 

For mean piston speeds of about 600 ft. niin., which is quite 
common practice, the proportions will be about as given in the 
following tables: — 



Area of Passage -f- Area of Piston 


1 


Type of Engine 


High Speed 


Corliss 


Valve opening to steam 
Exhaust Passage (cyl.) 
Steam Passage (cyl.) 


1 

JL 
13 

1 

To- 


t 

1 

9 


Diameter of Pipe -e- Diameter of Cylinder 


1 


Type of Engine 


High Speed 


Corliss 


Steam Pipe 
Exhaust Pipe 


1 

3 

4 

T7 


1 

3 
4 

10 




From Beaton and Rounthwaite's "Pocket Book of Marine 
Engineering" the following is quoted as applying to marine en- 
gines: — (H. P., M. P. and L. P. refer respectively to the high, 
mean, and low pressure cylinders of triple expansion engines.) 



46 



"The following figures give such speeds of steam as are 
usual in triple engines of the best class; but it must be under- 
stood that in dealing with very high piston speeds (say over 900 
feet per minute), it is not always either possible or advisable to 
give such large areas: 



then- 



SPEEDS OF STEAM. 

Main steam pipe, 8,000 feet per minute; or say 8,100 feet, 

Dia. of H. P. cyl. 



Diameter = 






90 


- + V 


Mean of max- 


H. 


P. 


7,500 ft. 


per miu 


Tuum valve open- 


M. 


P. 


9,000 


(( 


ings. 


L. 


P. 


12,000 


« ( 


Ports (during 


H. 


P. 


5,800 


i( 


•exhaust). 


M. 


P. 


7,200 


(< 




L. 


P. 


8,600 


( < 


Exhaust pipe 










•or passage from 


H. 


P. 


4,500 


< ( 


•one cylinder to 


M 


. P. 


5,500 


(< 


next or to con- 


L. 


, P. 


7,000 


( ( 


denser. 











+ v^Mean piston speed 



Nearly equivalent to 40, 
50, and 60 c. ft. of cyl- 
inder per sq. inch of 
port per minute. 



Ports (during H. P. 5,800 
exhaust) in light, M. P. 8,600 
high-speed engines. L. P. 11,500 



Nearly equivalent to 40, 
60, and 80 c. ft. of cyl- 
inder per sq. inch of 
port per minute. 



For Two-stage or Compound engines use the above figures, 
only omitting those referring to M. P. cylinders." 

In the case of multiporting, the aggregate area is usually 
made a little larger (say 10 per cent.) than for a single port. 

The lengths and widths of the ports are usually the same 
as those of the passages, but when the valve has an auxiliary port, 
as in the Sweet and some other valves, the widths must be ia- 
-creased, as will be seen later. 

The effective width of opening is of course equal to the area 
divided by the length. 

The length of opening for flat slide valves is from 8-10 to 
once the diameter of the cylinder, the former value being used 
when the opening of the steam pipe into the steam chest is so 
located that a wider valve would obstruct the passage. On Cor- 
liss engines the length is usually the same as the diameter of the 
•cylinder. In the case of piston valves the length of port is the 



47 



circumference and this is made from 2 5 to 60 per cent, greater 
than the diameter of the cylinder, the latter value corresponding, 
to a diameter of valve (about) equal to half that of the cylinder. 
This increased length permits narrower width of opening and 
shorter valve travel; or when the opening is not very effective on 
that side of the valve which is away from the cylinder, as is 
sometimes the case, it provides an increased area. If the valve 
bushing has bridges across the ports, allowance must be made fcr 
the consequent reduction of tht effective length of port, which 
may be from 2 5 to 35 per cent. 

34. CLEARANCES. The linear distance between the P'"s- 
ton and cylinder head, when the former is at the end of the 
stroke, is called the mechanical clearance. One-eighth inch or 
more may be allowed for inaccuracy of parts and faulty initial 
adjustment, and from 1-32 inch to 1-8 inch may be allowefl' 
for the wear of each bearing (usually three) affecting the 
clearance. In the better class of stationary commercial engines 
the clearance is from %" to ^", the former value being used 
when both the piston and cylinder head have machined faces 
and the latter when this is not the case. On vertical marine 
engines from 50 to 100 per cent more clearance is allowed at the* 
bottom of the cylinder than at the top, as the adjustment for 
wear in bearings decreases the space at the bottom. 

The clearance volume is that space which must be filled with 
steam when the piston is at the end of the stroke, and includes 
the volume between the piston and the cylinder head and thai 
in the passages out to the valve faces. It is usually expressed as 
percent of the volume displaced by the piston in one stroke. On 
stationary high speed engines it is usually from 6 to 13 per cent., 
on low speed engines from 2 to 6 percent, and intermediate be- 
tween these values on medium speed engines. 

On marine engines with flat valves the clearance for large 
cylinders is from 8 to 14 per cent, at the H. E. With piston 
valves the clearance is usually from l^^ to 2 times that of flat 
valves. Vertical marine engines have larger clearance at the- 
bottom than at the top on account of the greater mechanical 
clearance. 

Clearance is objectionable, but unavoidable, and should be 
made as small as possible. It may be reduced by making the 
passages shorter and more direct, and by reducing the mechan- 
ical clearance. For a given clearance volume and diameter of 
cylinder, the percentage of volume is less on long stroke engines 
than on short. With certain types of valve gear, as will be seen 
later, to prevent excessive compression large clearance is neces- 
sary. 



48 



35. DRAWING HYPERBOLIC EXPANSION LINES. First 

Method. Start with the X and Y axes, Fig. 38, and using abso- 
lute pressures and volumes as co-ordinates, locate the point of 
cutoff, c, and draw the vertical line cc'. Through any point 1 in 
the line cp produced, draw 01 from the origin, to intersect cc^ at 



V. . 





Fi&3a' 



^ 



2. Then the vertical and horizontal lines drawn respectively 
through 1 and 2, intersect at 3, which is a point on the expansion 
curve. Other points may be found in the same manner. 

Starting at k, the beginning of compression, draw the vertical 
line kk^ Through any point, 4, on this line, draw 04 from the 
origin to intersect the back pressure line kb at 5. Then the hori- 
zontal and vertical lines drawn respectively through 4 and 5, inter- 
sect at 6, which is a point on the compression line. The pres- 
sure at the end of compression is found by first determining the 
point of intersection 7 between Oo and kk^ and then from this 
point drawing horizontally to intersect the clearance line at 8. 

Second Method. To construct a hyperbola through the point 
b. Pig. 39, draw any line through this point to intersect the axes 
at a and a'. Along this line from a lay off a distance equal to 
ab, locating the point b', which is a point on the hyperbola. 

36. CUSHIONING THE RECIPROCATING PARTS. First 
suppose there is no compression. Then when the piston ap- 
proaches the end of its stroke the effective steam pressure and 
the inertia of the reciprocating part are both acting towards 
that end of the stroke, taking up the slack in the bearings of 
the reciprocating parts. Now, when the steam is admitted on 
the other side of the piston the pressure on the bearings -s 
rtversed more or less suddenly. With reciprocating parts of 
small weight, and with high steam pressure, this reversal will 
be very sudden and if there is much "play" in the bearings, ana' 
there must always be a little, the consequent impact will not 
only produce noise but will cause excessive stresses in the im- 
pinging parts. 

One method of preventing the occurrence of these unde- 
sirable features is to make the weight of the reciprocating parts 



49 

so great that their inertia will oppose the steam pressure suffi- 
ciently to cause the plaj' in the bearings to be taken up gradually, 
thus preventing impact. But as the inertia forces are free forces 
which tend to move the engine on its foundation, it is usually 
desirable to have them small, even when counterbalancing is 
attempted, so this method is usually unsatisfactory. 

Another method is to arrange the valve to open gradually, 
hut this is accompanied by a more gradual cutoff, which is unde- 
sirable. 

The best method is to gradually reverse the pressure on the 
bearings by introducing compression, then, when admission takes 
place there is no play to be taken up and consequently no impact 
in the bearings. 

The force due to the inertia of the reciprocating parts is 
greatest when the crank is on the H. E. dead center, and, as the 
steam pressures used are expressed as intensities per square inch 
of piston, the inertia force will be expressed in the same way. 
Without going into the derivation of the formula, the maximum 
inertia force per square inch of piston is 

wRN'^ 1 

m which w = total weight of reciprocating parts (in lbs.) 

divided by the area of the piston. 
This is from 2 to 3>^ lbs., the larger values being 
for the longer strokes and larger engines. 

R = radius of the crank (inches). 
N = revolutions per minute, 
n = ratio of length of connecting rod to crank radius 

Now if V is the piston speed in ft. minute, then 
12 V = 4 RN, or RN = 3 V 

Substituting this value of RN in equation (4) we get, 

w V N 1 

'^ = TL^(l+n' (5> 

Then if the piston speed is about 600 ft. minute, 

h = w N--16.8, when n = 6 . . . (6) 

= w N--15, when n = 5>^ . . . (1) 

37. COMPRESSION. The final compression pressure 
should not be greater than the initial steam pressure, and to 
cushion the reciprocating parts sufficiently to reverse the pressure 
on the bearings, it must overcome the pressure of steam on the 



50 

other side of the piston as well as the inertia force of the recipro- 
cating parts. Expressed algebraically 

> 
k = b + h < p (8) 

In which k = steam pressure at the end of compression. 

b = " '* on opposite side of the piston. 

h = intensity of inertia force (equations 4 to 7.) 

p = initial steam pressure. 

Having found k it is still necessary to determine at vxhav. 
point in the stroke compression should begin to reach this pres- 
sure. 

Let X = % of stroke for compression to begin 
b =: back pressure 
c = clearance volume % 

Then assuming a hyperbolic compression line and using 
absolute pressures, 

kXc = bX(c + x) . . . . (9) 

k X c 
or X = ^ — c (10) 

The same thing may be found by graphical construction, of 
course. 

When there is low back pressure, (such as occurs on con- 
densing engines) accompanied by large clearance, it is some- 
times not possible to get sufficiently high pressur'i^s at the end 
of compression, and then other expedients must be adopted for 
cushioning, such as employing a gradual lead, by having the edge 
of the valve oblique with that of the port, or by drilling through 
the valve small holes which open a little before the edge of ihe 
valve does. 

Compression should never be sufficient to lift the valve off 
its seat. In the case of the variable eccentric, the Stephenson 
Link and other similar valve gears, the compression iiicreases aa. 
th« cutoff is reduced, so it is necessary to investigate the compres- 
sion pressure corresponding to the earliest cutoff in this respect. 

On vertical engine it is advisable to have the compression at 
the bottom of the cylinder greater than at the top, as, besides the 
inertia of the repicrocating parts, their weight must be counter- 
acted. 



51 



38. RELEASE should occur from 2 to 15 per cent, from 
the end of the stroke depending on the speed of the engine. 

As release and compression are conjugate events v.'hen oper- 
ated by the same valve, if one is fixed, that determines the other. 
Often it is not possible to have both these events occur as desired, 
in which case a compromise must be made. 

39. LEAD. As the clearance must be filled and as a large 
percentage of the steam is condensed by the walls of the clear- 
ance space when admission takes place, it is usually necessary to 
give 'the valve lead. The smaller the compression is and the 
greater are the clearance volumes and the speed, the larger must 
be the lead. When the compression is up to the initial steam pres- 
sure, very little lead is needed. Sometimes no lead, or even 
negative lead is used. 

Another effect of lead is to increase the earlier valve open- 
ings, in the case of the variable eccentric and the link gears. This 
feature may be especially valuable, for when these gears operic^ 
at the earlier cutoffs the openings are very restricted. 

It is diflScult to give rules for lead as practice varies widely. 
For high speed engines it may be made 1-16 inch for each inch 
of radius of the eccentric, which corresponds to a lead angle of 
about dV2 deg. (slope 1:16), although double this amount is 
sometimes used. On large marine engines with large clearances 
the angle is even as large as 12 deg. at the H. E. On vertical 
marine engines the lead at the bottom is usually from 50 to 100 
per cent, larger than at the top, to make provision for the de- 
crease in lead at this end due to wear of valve gear parts, and to 
fill the larger clearance volume at this end of the cylinder. 

40. CUTOFF. When a simple D-valve is used, cutofiT 
should occur not much before % stroke. (See 28.) On high 
speed engines, on which the early compression and release 
are not so objectionable, and on which special valves are used, 
the normal cutoff is usually at V4, stroke, with a range from 
to 1/^ or % . The cutoffs for medium speed engines are about 
the same as for high speed. On Corliss engines the normal cut- 
off is from 1-5 to 1-4 stroke, with the tendency toward the 
former value for single eccentric gears and toward the latter when 
double eccentrics are used. In the case of link gears the latest 
cutoff is from % to % stroke, usually, and the normal cutoff is. 
later than i/^ stroke. 



•52 




U \ 



Fis.40 



41. DRAWING A D-VAIiVE. It is better to draw the valve 
In its central position, as shown in Fig. 40, for the H. E. The 
edges of the valve, of course, overlap the edges of the ports by 
amounts equal to the laps. To provide proper passage for the ex- 
haust steam the height h of the cavity in the valve must not be 
less than the width of passage w; and when the valve is to the 
extreme right, the distance AB should be at least equal to w. 
The bridge C should be wide enough for steam tightness when 
the valve is to the right and to have sufficient surface to prevent 
wear. It is not usually less than the thickness of the cylinder. 
G should be wide enough to prevent the exhaust edge from over- 
traveling when the valve is to the extreme left and should be 
narrow enough to let the steam edge of the valve overtravel some, 
so as to prevent wearing a shoulder. 

Rough Rules for the thickness of metal in the valve are 

t =r >^T to ^ T (11) 

t' =.8T to .9T (12) 

in which T is the thickness of the cylinder wall, and t and t' are 
the thicknesses shown in Fig. 40. For stationary commercial 
engines Professor Barr gives 

T = .05 (cylinder diameter) + .3 . . (13) 

the unit being inches. 

If the valve is not "balanced," it is desirable to make it a& 
small as possible, so as to reduce the friction and' weight to the 
minimum. Consequently the valve is laid out to give the nar- 
rowest width of exhaust cavity and this may be done in the fol- 
lowing manner: — 

Having drawn the valve seat and having determined the face 
of the valve F at one end of the cylinder, say the H. B. as in 
li'ig. 40, move the valve to the extreme right and lay off the 



53 



■proper distance from its exhaust edge A to locate B. The draw- 
ing of the valve and seat can then be completed readily. 

When the valve is central its center line coincides with that 

•of the valve seat, which is usually made symmetrical.' If the laps 
of the two ends are not equal, the valve will be unsymmet- 
rical. Then in determining the shortest allowable exhaust cavity 
that end of the valve which has the greatest exhaust lap (algebra- 

-ically) is the one to be considered. 

Piston Valves may be considered to be flat valves bent into 
cylindrical form. They are 
laid out in just the same man- 
ner as flat valves. 

LfOoking at the end view 

in Pig. 41, it is seen that the 

steam, which issues from the 

nipper semi-circumference of 

the valve, must go through 

the passages bb to reach the 

'Cylinder. The effective areas 

'Of these passages b are shown 

in the section in the upper left 

hand corner of the Figure. 

Their combined area should' be one-haif that needed for the 

•exhaust. 

If a bush is used for the valve seat, its thickness may be 

t = ^" + D/30 (14) 

in which D is the diameter of the valve in inches. If bridges are 
used across the port, their width may be made a little greater 
than their thickness (say 20 per cent.) and, to distribute the wear 
more evenly, they may be made oblique (usually 60. deg.) with 
the edge of the valve. 

Internal Valves, whether flat or piston, may be "laid out" in 
a similar manner, the only difference being that the steam and 
exhaust laps change places. 




rLS.4i 



Part II 



VALVE GEAR FOR HIGH SPEED ENGINES 

MULTIPORTED AND BALANCED VALVES 
SHAFT GOVERNORS 
VARYING ECCENTRIC 



CHAPTER I. 
INTRODUCTION. 

42. VALVE GEARS FOR HIGH SPEED AUTO>LlTIC 
ENGINES. — (a) The High Speed type of engine was briefly 
described on page 40. In general, these engines have auto- 
matic regulating devices which cause them to develop just 
snough power to meet the demand and at the same time maintain- 
approximately constant rotative speeds at all loads. The regula- 
tion is accomplished by a "Shaft Governor," which controls the 
point of cut-off by varying the position of the eccentric with 
respect to the crank, 

b. The "range of cut-off" is usually from to % or % 
stroke, and the "range of load" is from "friction load" to 50 per 
cent (and sometimes even 100 per cent) "overload," this ^atter 
heing with respect to the "normal load" or load at which the 
engine usually operates. The normal load should of course be 
that at which the engine gives the best economy in the con- 
sumption of steam, which, for simple engines, corresponds to a 
cut-ofiE at about i/4 stroke. 

On page 39 it was seen that if a simple slide valve is used 
to give a cut-off as early as ^/4 stroke, there will be introduced 
certain features which are usually undesirable. How these fea- 
tures can be overcome or be used to advantage in this type of 
engine, will now be considered. 

c. It was seen that the early cut-off is accompanied by an 
early compression which results in a terminal pressure which is 
ordinarily objectionably high. This terminal pressure can be re- 
duced, however, by increasing the ratio between the clearance 
volume and that displaced by the piston. With a given clearance 
volume and piston area, this clearance ratio may be made large 
by using a short stroke. Hence, engines of the type under con- 
sideration are made with relatively short strokes (usually from 
one to one and a third times the diameter of the cylinder). 

Q201. Given, clearance volume 30» cu. in., 
diam. of cylinder 16 in., stroke 36 in., back pres- 
sure 17 lbs. absolute, and compression beginning 
at 70% of stroke. 

(a) What is the per cent, clearance volume? 
(b) What is the pressure at the end of compres- 
sion ? 



62 

With the same data except that the stroke is 
18 in., 

(c) What is the per cent, clearance volume? 

(d) What is the pressure at the end of com- 
pression? 

If an engine runs at a high rotative speed, a fairly high 
compression, instead of being a fault, may be a necessity, Itj 
order to properly "cushion" the reciprocating parts. Further, 
with this high speed, the early release (which accompanies the 
early cut-off) is a desirable feature, whersas on a low speed 
engine it would be objectionable. Hence these engines are nn» 
only 'short stroke," but are also "high speed." 

Q202. Given, the weight of the reciprocating 
parts, per sq. in. of piston, as 214 lbs., stroke 36 
in., R.P.M. 100, and length of connecting rod equal 
6 cranks. 

(a) What is the inertia force of the recipro- 
cating parts (per sq. in. of piston) at the head 
end of the stroke? (See §36). 

(b) Same except with stroke 18" and R.P.M. 
200? 

(c) Is the terminal pressure found in Q201d 
sufficient to overcome this inertia? 

d. The excessive size of the valve gear parts, which ordin- 
arily occurs when a valve is designed for an early cut-ofC, may 
be overcome by increasing the length of port which calls for a 
narrower valve opening and a corresponding reduction of the 
laps, travel, and s'ize of the eccentric; and these in turn are ac- 
companied by a decrease in the friction and wear of the valve 
gear. The greater length of port may be obtained by using a 
wide valve, or by using a multiported valve. 

With the type of valve gear which is used on- this class of 
en.gine, the travel of the valve varies with the cut-offs and 
the earlier the latter are, the more restricted are the openings of 
the valve. When the openings are ample for the latest cut-offs, 
auxiliary ports may be added to the valves in such a mannpr 
as to assist during the early openings only, and to have little 
or no effect on the wider openings. 

Sometimes special kinematic arrangements of the valve 
gear are employed to give wide openings with small travel, bul 
this is at the expense of complication of mechanism. Examples 
of these various types of valves will be given later. 



63 

e. The friction of tlie valve is undesirable not only because 
it decreases the mechanical efficiency of the engine, and causes 
wear, but also because it disturbs the action of the shaft gover- 
nor. The work done against friction may be reduced by de- 
crsasing the motion and by lessening the pressure between the 
face of the valve and its seat. The pressure of the valve on its 
seat may be due in part to the w^eight of the valve, but it is 
principally caused by the steam pressure. The back of the valve 
is subjected to the pressure of the live steam, whereas a part of 
the face is exposed to the exhaust pressure, the resulting or un- 
balanced pressure forces the valve against the seat causing the 
friction and wear. To reduce this unbalanced pressure to a mini- 
mum, various schemes of "balancing" the valve are employed. 
The simplest scheme is to use a piston valve, which is subjected 
to equal pressures on opposite sides and is therefore balanced be- 
cause of its shape. Other means of balancing, which will be 
described later, are to use "balance or equilibrium rings," "bal- 
ance or pressure plates," and by using a "floating valve." 

f. On vertical engines whan the weight of the valve gear is 
great, there are sometimes attached to the upper end of the 
valve stem "balance pistons," which are of such size that the 
£team pressure on the bottom side will carry the weight of th? 
\alve gear parts. 

g. The inertia of the valve gear parts, which adds to the 
friction and wear and disturbs the action of the governor, may 
be reduced by making the valve and gear of light weight. 

h. In case there should be water in the cylinder during the 
compression phase, in quantities more than sufficient to fill the 
clearance volume, relief of some kind must be offered, otherwise 
some part of the engine must break or yield. "Relief Valves." 
which are somewhat similar to boiler safety-valves, are frequent- 
ly used, but often the slide valve itself may be arranged to lift 
off of its seat and afford sufficient relief. 

SUMMARY. It is evident from the foregoing discussion 
that one must be familiar with the arrangements and methods 
of operation of shaft governors, with the special types of 
valves, and with the action of the variable eccentric before 
one can undertake the design of a valve gear for a high speed 
engine. These features will therefore be considered next, but 
only the more typical cases will be taken up. The student should 
suppliment the text by a study of the catalogues and drawings 
of the various manufacturers. 



CH.1PTEII II. 

TYPES OF VALVES USED OX HIGH SPEED ENGINES. 

43. In studying the valves discussed in this chapter note 
the following features: 

(1) Relative Sizes and Weights (inertia effect). 

(2) Methods of Multiporting and Auxiliary Porting. 
(8) Methods of Balancing. 

(4) Provision for Water Relief. 

(5) I-Tow wear is taken up and provision for re-machining. 



Sy^fj''^ 




44. SIMPLE DIVIDED VALVE. If a cylinder is long and 
has direct passages, the valve as ordinarily constructed would 
be of excessive size and weight. Fig. 42 shows how these unde- 
sirabl3 features may be avoided by making the valve in two 

parts. 




65 

45. DOUBLE PORTED MARINE ViLLVE. Figure 43 
shows a valve which is double ported to both the steam ar^d 
the exhaust. The steam enters the cylinder past the end of the 
valve and ?.lso through the port x, which latter is supplied 
through a passage opening from the side of the valve. The ex- 
haust takes place past the inner edge and also through the 
port y. 

(a) If the back of the valve is subjected to the pressure of 
the steam, and a part of the face of the valve is exposed to the 
exhaust pressure, the resulting unbalanced force presses the 
valve against its seat causing friction and wear as movement 
takes place. In order to reduce these undesirable features, it is 
necessary to protect a sufficient area of the back of the valve from 
the steam, to "balance" the valve. In this case this balancing is 
accomplished by employing a steam tight "balance or equilibrium 
ring," which is fitted in the steam chest cover and held against 
the back of the valve by springs. The space inside this rmg is 
open either to the atmospliere or to the exhaust. The valve 
should not be completely balanced, for it should press against 
the valve seat with sufficient force to maintain a steam tight 
joint. In case there is water in the cylinder this valve can lift off 
of its seat and afford a relief. The valve is here shown to ride 
on a ^'false valve seat," which can be replaced when worn. Also 
t?ie metal at the face of the valve is made with extra thickness to 
allow for remachining. 

(b) Proportions. Since the valve is double ported, the 
portwidths, laps and travel will be only half those which would 
be used on a single ported valve. In Fig. 43 the steam and ex- 
haust laps are S and E. The passage W must of course be wide 
•enough for the exhaust steam. B should be wide enough tc 
maintain a steam tight joint, and G should be equal to the travel 
of the valve plus B, in order that B will not overtravel into 
either port. When the valve is central, B should be in the mid- 
dle of G. The thickness of metal of the valve may be made the 
same as for a simple valve. (See page 52). The thickness of the 
False Valve Seat may be made the same as that of the cylinder 
wall or greater. 



66 



X201. Draw a section of a Double-Ported 
Marine Valve, in its central position, making S 1 
in., E Va in.. W l^^ in., B % in., throw 1% in. 
Only one end of the valve need be drawn. 




(c) In the Elliptical Diagram (Fig 44) the ordinates of 
the portion which is sectioned vertically represent the openings 
of a single ported valve. The openings occuring when the valve 
is double ported are shown by the ordinates of the areas whiea 
are sectioned horizontally. 

The double-ported openings can be shown on the Zeuner and 
the Sweet Diagrams in a somewhat similar manner as shown by 
curves A. 9 C. in Figs. 57 and 58. 

X202. Given diameter of cylinder 18 in., 
stroke 24 in., R.P.M. 150, length of port 18 in., 
cut-off % stroke, lead Vs in., and compression be- 
ginning at 85% of stroke. For a Double-Ported 
Marine Valve — (a) Compute the width of open- 
ing to steam, using 8,000ft. min. as the velocity 
of the steam. Also determine the width of port 
using 5,500 ft. velocity of the exhaust. 



67 



(b) Draw a Bilgram Diagram. 

(c) Draw a longitudinal section of the valve. 

(d) Draw an Elliptical Diagram, showing 
the double-ported action. 

(e) Draw Zeuner and Sweet Diagrams, and 
on them show the double openings. 




r><9.4-5 



46 BALL TELESCOPIC VALVE. The valve, shown in Fig. 
45, is really composed of two valves, each having its own seat, 
and each having on its back a cylindrical portion which telescopes 
with the similar part on the other valve, the joint of coursa being 
steam tight, but permitting relative movement. Steam is ad- 
mitted into the middle of the valve and is exhausted at tha ends. 
The valve is practically balanced, as each part acts as a 
balance ring for the other; however, there is enough unbalanced 
pressure to maintain steam tight joints at the valve seats and 
also to take up the wear. Exhausting at the ends has the ad- 
vantage that the stuffing-box for the valve stem, is subjected 
to the pressure of the exhaust steam only and is therefore much 
easier to keep tight. In case there is water in the cylinder the 
parts can lift ofC of their seats to give relief. The ports are 
3iecessarily long and circuitous and the clearance volume large. 



68 



^TJTffr^ 






Sx/iffUST 



(CL) 



M ^ 



"1^^ 




47. AliliEN OR TRICK VALVE. This valve has an auxil- 
iary passage aa' (Fig. 46a), so arranged that, as the valve moves 
to the right, it opens at f at the same instant that the main steam 
edge opens at y to admit steam. The exhaust is single ported.* 

(a) Considering the valve as moving to the right, the 
phases of opening of the steam edge are as follows: (1) T!ie 





' 






Sj^/ o£: 


1- 


fci — 






r^^ n 


cife 



* The student is advised to construct a model of a symmetrical valve similar to 
that shown in Fig. 47, using two pieces of stiff paper, one piece 3 inches by 6 inches 
and the other 1 inch by 8 inches. Referring to Fig. 50, for dimensions use W %. 
inche, N 1-16 inch, E Vs inch, S and S^ 5-16 inch, B Vs inch, C K inch and I iH 
inches. This model will assist greatly in gaining an understanding of the further- 
discussion. 



69 



double ported action (Fig. 46a), caused by y and f opening at 
the same rate, continues until a is wide open. (2) With the 
movement continuing, (Fig. 46 b), the opening at y continues to 
increase while that through a remains constant, i.e., the opening 
is *\single ported plus a constant." This phase continues until a', 
the left end of the auxiliary passage, begins to be throttled by the 
exhaust edge of the valve seat, as in Fig. 46c. (3) With further 
movement to the right, a' is throttled at the same rate as the 
main steam edge opens, the effective opening remaining constant 
until the auxiliary passage is entirely closed. (4) After this 
the opening is single ported until the cylinder port is wide open. 
Now if the valve moves to the left to close, the effectiv 
opening will decrease with these phases occuring in the reverse 
order. 




Fks 46 



(b). A Diagram of Openings for the steam edges is given 
in Fig. 48, the elliptic curve AMC* showing the opening of edge y 
alone, and 1 — 2 — 3 — 4 etc. showing the total effective opening. 
If y is the ordinate of the former curve and y' that of the latter, 
then, taking the phases in order, as numbered in the preceding 
paragraph, the values of y' will be as follows: (1) y' — 2y, 
(2) y' = y + a, where a is the constant opening through tlie 
auxiliary port; (3) y' = constant. = W — B, where W is the 
width of port and B is the width of metal at the end of the valv^^, 
(see Fig. 50); and (4) y' = y. The maximum opening of the 
main steam edge is m. 

The Zenner and Sweet Diagrams are indentical with those 
shown in Figs. 57 and 58 and are described in Par. 51h. 

(c) Case I. If W ^- B + m, the case is that which has 
already been discussed. 



^ 



* Purposely shown distorted. 



70 



(d) Case II. If W = B + m, lines 3 and 5 will be tangent 
to AMC at M. 

(e) Case III. If W = B + m + a, curves 2 and 6 will meet 
at 8. 

(f) Case IV. If W = B + (the total desired opening w'), 
and if a = m = ^ w', then, the opening is double ported through- 
out, and curves 1 and 7 will meet at 9 with ordinate 2 m. It would 
appear at first that, since the steam opening is double ported, the 
steam lap and travel could be made half thosa required for a 
simple valve; but, as the exhaust is single ported, the opening 
of this edge may then be too restricted. Hence, it is necessary to 
find the throw which will give the desired opening to steam, and 
also that for the proper exhaust opening, and then use the 
larger of the two. 

X203. Given: — Exhaust opening 1% inches; 
total steam opening at least 1^/4 inches; lead % 
inch; C. O. % stroke; compression 85% stroke; 
Allen valve with width of auxiliary port half the 
required opening to steam. 

Required: — Throw, angle of advance, steam 
and exhaust laps for the head end of the valve. 
Draw the Diagram of Openings. 



Y' ^r 



a 




/;. 



(g) Considering the head end of the cylinder, after the valve 
has moved to the left far enough to cut-off the steam at y, (Fig. 
46), the auxiliary port, now closed at f, is still open to the head 
end of the cylinder at a', hence the expansion takes place with a 
clearance volume equal that of the cylinder plus the volume of 
the auxiliary passage. After this passage is closed by the valve 
moving farther to the left, the expansion is with the clearance 
volume of the cylinder alone. Fig. 49 shows an indicator card on 
which the closing of the auxiliary port is shown at r. After ex- 
haust closure, the compression is first into the clearance of the 



71 

cylinder, and later it is also into the passage in the valve. In 
Fig. 49, the opening of the auxiliary port occurs at b. 

OY is the axis for expansion and compression when the 
auxiliary passage communicates with the cylinder; and O'Y' is 
the axis when expansion takes place in the cylinaer alone. The 
horizontal distance between the axes represents the volume of the 
auxiliary passage. Hyperbolas Cr and Ab are with respect to 
axis OY, while rR and bK are drawn with O'Y' as axis. 

(h) In the foregoing paragraph it was assumed that the 
exhaust edge closed before the auxiliary port opened, i.e., that G is 
greater than W in Fig. 50. If G is just equal to W, then on the 
indicator card r will coincide with R and b with K. Unless G 
is equal or greater than W, release will occur prematurely 
through the auxiliary passage into ths other end of the cylinder, 
which is stil/ open to exhaust at this time. 

(i) Negative auxiliary lap (N and n, shown positive in Fig. 
50) may be used if the valve has positive exhaust lap, but from 
the preceedmg paragraph ( — N) must not be greater than (H-E) 
nor ( — n) greater than e. From the time the auxiliary port opens 
at one end until it closes at the other, the valve movement is N 
plus n, and during this time there is communication between the 
two ends of the cylinder with a resulting equalization of pressure. 
Fig. 49 shows by the broken lines the changes in the indicator 
card for this case. The communication is established when ex- 
pansion has reached r, and compression b, the line of equalized 
pressure being d-g. Communication ceases at e and h. It is seen 
that the cushioning effect is increased with this arrangement and 
sometimes this is a very desirable feature, as in the case of a 
condensing engine in which conditions are such as to limit the 
compression to less than the desired amount. 

X204. Using the data of X203, and with 
negative auxiliary lap % inch, find the piston posi- 
tions for the beginning and closing of communica- 
tion between the two ends of the cylinder and draw 
a theoretical indicator card, with clearance of cylin- 
der 4% and in auxiliary passage 4%, steam pres- 
sure 100 lb. gage, back pressure 2 lbs. absolute. 
Neglect the angularity of the connecting rod. 
(j) Proportions: For notation see Fig. 50. 

w' — is the desired width of opening to steam (total). 
w — is the desired width of opening to exhaust (total), 
m— -is the maximum width of opening of the main 

steam edge, 
a — is the width of the auxiliary passage. 



72 




If the auxiliary port does not increase the maximum open- 
ing of the valve, but merely augments the initial and final 
openings (as in Cases I. and II.) the throw, lead and laps will 
be the same as those found for a single ported valve. The 
amount of opening during the third phase (that of constant 
opening) may be arbitrarily assumed at any suitable value k; 
then W=k-fB, but must, of course be greater than w. 

The width of the auxiliary port (a) may be made anything 
within reasonable limits. I-t must be wide enough to permit the 
use of a core of thickness sufficient to withstand the flow of the 
molten metal when the casting is poured, and for this, the width 
should usually be somewhat greater than the thickness of metal 
in the valve. 

To receive the full benefit of the auxiliary port during the 
whole of the period of opening, W must be at least equal to 
B+m+a, as in Case III. 

To have double ported action during the whole period of 
opening, not only must W be equal to B+W, but (a) must equal 
V2^'. The throw would be that of a double-ported valve, pro- 
vided it gives sufficient opening to exhaust, as in Case IV. 

In addition, it must be seen that: — 

S' = S and s' = s 



G and g 



W 



The thicknesses of metal may be the same as for a simple 
valve, (pg 52) or thinner if well ribbed. 

X205. Given, diameter of cylinder 18 in., 
in., stroke 24 in., R.P.M. 150, length of port 18 in., 
cut-off % stroke, lead % in., and compression 85% 
of stroke. For an Allen valves, which is to have 
double-ported openings to steam during the whole 
period of opening: 

(a) Compute the widths of openings to steam 



73 



and exhaust, using for velocities of steam 8,000 
and 5,500 ft. min., respectively. 

(b) Draw a Bilgram Diagram. 

(c) Draw the longitudinal section of the 
valve. 

(d) Draw a Diagram of Openings for the 
steam edges. 




F/Q.S/ 



48. DIVIDED ALLEN VALVE. This is shown in Fig. 51 
and is the equivalent of the ordinary Allen Valve. 




r,<^5z 



49. GIDDLNGS FLOATING VALVE. This valve is obtained 
by adding the hood C in Fig. 52 to the divided Allen Valve of Fig. 
51. The hood in no way affects the valve events; it is added for 
the sole purpose of balancing the valve. When the steam is 
first admitted inside the hood, the valve lifts from its seat 
letting steam into the steam chest until the pressure there is suf 
ficient to reseat the valve. The valve then tends to float but the 
pressure on the back is always suflScient to keep it seated. To 
avoid the lifting of the valva, which lets some of the steam escape 
to the exhaust, little "needle valves" (a) and (b) are added in 
such a way as to maintain the proper pressure on the back of the 
valve to balance it. One of these needle valves connects the out- 
side of the valve with the exhaust and the other with the steam 
passage. 



74 




50 ARlvnNnTON and SIMS VALVE. Piston valves can be 
made like the Allen Valve. Fig. 53 shows tha Armington and 
Sims valve which is of this same type, but is arranged to take 
steam at the middle and exhaust at the ends. 





Fig 54 



51. SWEET VALVE. Fig. 54 shows an "auxiliary-ported'* 
valve which is of the ''pressure-plate" type used by Prof. John 
E. Sweet on his Straight Line Engine. The valve, which is some- 
times called the "Straight Line Valve," is really a rectangular 
piston valve which slides between the valve seat and a balance- 



75 

plate, or pressure-plate, which latter is supported by top and 
bottom distance-pieces so as to just clear the valve. The valve 
is double-ported to steam and exhaust, at least, during part of 
the period of opening. All the sliding surfaces are ac- 
curately scraped so as to give sufficient clearance to permit 
the valve to move freely, but not enough to allow any 
leakage of steam. The pressure plate is held from moving 
endwise by dowel pins, or other device, which permit it to lift 
to afford a relief in case there is water in the cylinder. To re 
turn the plate to its seat, springs are provided on its back; and 
o,fter it is once seated Che steam pressure on the back holds it in 
place. Th«^ wear may .be taken up by scraping the edges of the 
distance pieces. The pressure-plate is made very thick to pre- 
vent it from deflecting enough to clamp the valve, the deflection 
being caused by the steam pressii*re on the back of the plate.. 
The valve takes steam at the ends and exhausts at the middle,, 
it is auxiliary-ported to both the steam and exhaust, is perfectly 
balanced, practically frictionless and wearless, affords relief to^ 
water and, being of the "skeleton" type is of minimum weight.. 
Prof. Sweet added the rib R to protect the surface of the- 
pressure-plate from any erosion which might be caused by the- 
impact of the exhaust steam. This rib also strengthens andi 
stijfens the end.* 

*The student is advised to construct a model of the Sweet valve similar to that 
shown in Fig. 47 for the Allen valve, using two pieces of stiff paper, one piece 3 
inches x 73^ inches, and the other 1 inch x 9 inches. Only the head end of the valve 
need be considered. The guide straps on the larger piece of paper should be 5 inches 
apart, and the steam edge of the valve seat should be 1/^ inches from the left strap. 
The end of the valve should be 3 in. from the left end of the slide. For dimensions . 
{referring to Fig. 60) use W 1 inch, S H inch, E 1-16 inch, B ^ inch, a K inch, C H 
inch (purposely made short), D % inch, throw 1 inch and thickness of valve meta 
5-32 inch. 



76 



(a) Referring to Fig. 55 and considering the valve as 
moving to the right, the phases of opening 

of the ste?m edge are as follows: (1) 
There is double-ported action (Pig 55a), 
caused by y and f opening at the same 
rate, until ihe opening at f becomes equal to 
that through the auxiliary passage (a). 
<2) With further movement (Fig. 55b), 
the opening at y continues to increase 
while that through (a) remains constant, 
i.e., the ;opening is single-ported plus a 
constant. This phase continues until (a) 
begins to be throttled by the exhaust edge 
of the valve seat. (3) With the movement 
continuing, (a) is throttled at the same 
rate as the main steam edge opens (Fig. 
55c), the effective opening remaining con- 
stant until the auxiliary passage is entirely 
closed. The extent of the opening is equal 
to the width of port (W) minus the width 
of the bridge-end (B) or (W — B). (4) 
After the auxiliary port is entirely closed 
(Fig. 55d) the opening is of course single- 
ported until the port is wide open. 

Now, if the valve moves to the left 
to close, the effective opening will decrease with these phases oc- 
curring in the reverse order. The opening to the exhaust may 
have some or all of these phases, depending on the proportions. 





Fiq56 



It is seen that the phases of opening are exactly the saD»e 
as in the case of the Allen Valve. 



77 

(b). A Diagram of Openings of the steam edges of 
the valve is shown in Fig. 5 6, in which the ordinates y 
of the elliptic curve AMC represent the openings of the 
edge y in Fig. 55. The ordinates of the curve 1 — 2 — 3 — 4 
etc. show the total effective opening, including that through the 
auxiliary passage. If y' is the ordinate of this curve, its value 
in the successive phases (numbered as in the preceding para- 
graph) is: (1) y' = y+f = 2y; (2) y' = y + a; (3) y' = 
W~B := const.; and (4) y' =r y. The maximum opening of the 
main steam edge is m. 

(c). Case 1. Tf W < B + m, the case is that which has 
iust been discussed. 

(d) Case II. If W = B + m, lines 3 and 5 will be tan- 
gent to AMC at M. 

(o). Case III. If W := B + m + a, curves 2 and 6 will 
meet at 8. 

(f). Case TV If W = B -f (the desired opening w') and 
if a =-- V2 w', the opening is double-ported throughout. Then 
for the steam edge the throw of the eccentric need only be one 
iialf that required for a single-ported valve. However, it may 
be necessarj"^ to use a larger throw to give sufficient opening 
lor exhaust. 

(g) With this valve, just as was the case with the Allen 
valve, the clearance volume is variable, that in the cylinder being 
augmented at times by that in the auxiliary passage in the valve. 
When a change takes place in the clearance volume the expan- 
sion line on the indicator card also changes, but with this vahc 
the change is usually so slight as to be negligable. 




Fid 53 



(h) . The Zeuner and the Sweet DiagTams, for the steam 
edges of the Sweet valve, are shown in Figs. 5 7 and 58. In these 



78 

diagrams the figures and letters correspond with those used in 
the preceding paragraph in connection with Fig. 56. These dia- 
grams also apply to the Allen Valve, the reference letters and 
figures being the same as those which were used in describing 
the diagram of openings for that valve (Paragraph 47b and Fig. 
48). 

(i) Loss of Steam. Considering the left end of the valve,^ 
if it moves far enough to the left so that the auxiliary-port 
travels beyond the end of the pressure-plate, this port fills with 
live steam and when the valve moves to the right again, tliis 
steam will be thrown over into the exhaust without doing work, 
because the exhaust edge is still open when the auxiliary-port 
opens to the cyl. passage. There are two ways of preventing this 
loss. One is to make the balance plate so long that the auxiliary 
passage will not overtravel. The other way is to make G wider 
than W in Fig. 60; then the live steam is transferred into the 
cylinder passage after the exhaust edge is closed, augments the 
compression and later is used during expansion. In this case, 
however, the exhaust is single-ported. To have double-ported ex- 
haust and at the same time have G greater than W there may 
be employed an auxiliary port for the exhaust, made separate 
from that for the steam, as a' in Fig. 59. This last arrangement 
is the original form of Sweet Valve. 



Fig 59 



Considering this last form of valve — if, as it moves to the 
right, admission takes place before a' is closed by the exhaust 
edge, this auxiliary passage will fill with live steam. Then, if 
the valve moves far enough to the right, so that a' opens to the 
exhaust chamber, this steam will be lost without its having done 
any work. There are two ways of preventing this loss: — One is 
to make D (Fig. 60) so wide that a' will not overtravel; the other 
is to so locate a' that it will be closed by the exhaust edge before 
admission occurs. 




79 




(j) Proportions. Referring to Fig. 60., B may be made 
any size that is consistent with strength and casting qualities. 

w = opening to exhaust. 

w' = opening to steam (total). 

m = max, opening of the main steam edge. 

For the meanings of the other letters see the figme. 

The height of pockets in the balance-plate and that of the 
^pace above the rib R must be at least equal to a. The height of 
Tib R above the main valve-seat must be at least w. Hence 
the depth of the valve must be at least H ^ w + t -f a. 

If the auxiliary-port does not increase the maximum open- 
ing of the valve, but merely augments the initial and final open- 
ings (as in Cases I to II) the throw, lead and laps will be the 
same as those found for a single-ported valve. The amount of 
-opening during the third phase (that of constant opening) may 
be arbitrarily assumed at any suitable value k; then W = k -\- 
B, but must, of course, be greate/r than w. 

The width of the auxilliary-port (a) may be made anything 
ivithin reasonable limits. It must be wide enough to permit the 
use of a core of thickness sufficient to withstand the flow of the 
molten metal when the casting is poured, and for this the width 
should usually be a little greater than the thickness of metal in 
the valve. 

To receive the full benefit of the auxiliary-port during the 
whole of the period of opening, W must be at least equal to 
B-f-m-f-a, as in Case HI. 

To have double-ported action during the whole period, not 
only must W be equal to B + w', but (a) must equal i^ w'. The 
throw would be that of a double-ported valve, provided it gives 
.sufficient opening to exhaust, as in Case IV. 

Provision must be made against carrying steam over into 
the exhaust, as explained in paragraph (i). 



80 




t 



iiU 



i^L_j^ 



Fig 6 



(k). StrengUi. The valve should be of the least weight 
consistent with strength, rigidity and casting qualities. The 
thickness of metal may be about one-third that of the cylinder 
wall (page 52), or t = (cylinder diam -^ 60) + .1" 

The valve is loaded on the ends by the steam pressure, as 
shown in F\g. 61a. The ends must be designed as beams. The 
addition of posts across the auxiliary-passage greatly strengthens 
and stiffens these ends, and if the valve is very wide one or more 
central bars should be added as shown dotted. The side strips 
which connect the two ends are compression members. 

The Pressure-Plate must be made very thick, otherwise it 
will deflect and clamp the valve. It is a beam (Fig. 61b) of 
length L, uniformly loaded by the steam-pressure and supported 
at the sides. The deflection should be limited to about .00 1'^ 
For such a beam the deflection is 



A = 5/384 



E I 



Where p = load per inch of length (steam pressure). 

L = length of beam, here a little greater than the; 

length of the port. 
E = 15 to 17 million for C.I. 
I = bh^ ^ 12. 
b = width of beam, 
h == depth of beam. 

A strip 1' wide may be taken, ( i.e. b = 1"). 

Over the exhaust cavity the thickness may be made less 
than h, as the deflection at this place will not interfere with the 
valve. 

Dowel pins, or other device, must be provided to keep the 
balance-plate in position and springs must be used to return the 
plate to its seat in case it should be lifted therefrom when there 
if? water in the cylinder. 



X206. Given, Cylinder diameter 16 in., stroke 
in., length of port 16 in., CO. % stroke, 



81 



lead Vs in., compression 85% of stroke, 
valve, Case I. 



Sweiet 



(a) Compute the widths of valve openings 
for both the steam and the exhaust, using for the 
respective velocities of steam 8,000 and 5,500 ft. 
min. 

(b) Draw a Bilgram Diagram as for a sin- 
gle-ported valve. 

(c) Assume the width of opening (k) dur- 
ing the third (or constant-opening) phase, as % 
of the maximum steam opening found in (a). Take 
B the thickness of the metal at the end of the valve 
as % in. Determine the width of port opening W. 

(d) Assume the width of the auxiliary pas- 
sage as % in. and draw a longitudinal section 
of the valve and balance plate. The thickness of 
this latter should be computed. Provide against 
loss of live steam. 

(e) Draw a Diagram of Openings for the 
head end of the valve. 

(f) Draw Zeuner and Sweet Diagrams. 
Similar problems may be devised for the 

other cases. 



SecT. ©S Seer A A 




Fiq.6Z. 



52. AVOODBURY VALVE. A valve of this type is shown 
in Fig. 62. It combines the Sweet and the Allen principles. 
There are auxiliary passages a and a', like those in the Sweet 
valve, but in addition there are also longitudinal ones a'', like 
that in the Allen valve. The opening to steam is quadruple- 
ported, the edge of the valve uncovering simultaneously at f, y, 
F. and Y. The opening to exhaust is double-ported. 



82 



4e f — 
o 
o 



O O O j o o o 
o 



I f75^1 j Imgt^ 



^ 



C^^ 



o o 



I2J 



^ ^^m 



o o 



o 
e+ 
o 
o 




^3tc•C7Volv ^-^ 



53. McEWEN (RIDGWAY) VAIiVE. Fig. 63. Instead 
of having the auxiliary passages in the valve itself, they are 
here located in the pressure-plate, as shown at (a) in the sec- 
tional views. The steam which passes the upper edge of the 
valve enters the passage (a), which connects with the auxilia^'y 
ports (a') in the valve seat. These latter openings connect with 
the main passages in the cylinder. The valve gives double-ported 
opening to both the steam and the exhaust. 




Fiq.64 



83 

54. CO^IPOUND VAIiVES. Fig. 64 shows a pair of valves, 
which are mounted on the same valve stem and which are so ar 
ranged as to distribute steam to the H.P. and L.P. cylinders of 
n cross-compound engine, the cranks of which are 180 degrees 
apart. The valves are piston valves of the simple "D" type. That 
for the H. P. cylinder takes steam from its middle, while that 
for the L. P. cylinder admits steam past its ends. 




Pica GS . 



Fig 65 shows a somewhat similar arrangement of a double- 
valve for a tandem-compound engine. There are simple 
'"D" valves for both the H.P. and the L.P. cylinders. The walls 
of the exhaust chamber of the H.P. valve are extended to form 
a hood, or steam chest around the L.P. valve. The passage X is 
open at the side of the valve and is filled with live steam. 

Piston valves similar to this last can be devised. 

55. WESTINGHOUSE COMPOUND VALVE. 

The Westinghouse compound 
engine is single acting, with 
cranks placed 180 degrees apart. 
One piston valve is used to dis- 
tribute steam to both cylinders. 
When this valve is in the position 
shown in Fig. G6, the steam is 
being admitted to the H.P. cylin- 
der through the port A, and ex- 
hausted from the L.P. cylinder at B. 

As the valve moves to the right, first, steam will be cut ofE 
at A, then the L.P. exhaust will be closed at B and finally C will 
establish communication between ports D and B, so that the H.P. 
cylinder will exhaust into the L.P. cylinder. 

As the valve returns to the left, first, the L.P. cut-off and 
H.P. compression will occur simultaneously, then L.P. release 
and finally H.P. admission will take place. 

E is a by-pass valve which is used in starting the engine. 




84 




1 



56. VAUCli>\lN VALVE. Fig. 67. This valve is used on 
compound locomotives, on which the H.P. and L.P. piston rods 
are attached to the same cross head, so that the pistons move 
in unison. Only one valve is used to distribute the steam to both 
cylinders. In the Figure both pistons are moving to the left. 
Steam is being admitted to the H.P. cylinder at A, and exhausted 
therefrom at B into the middle of the valve. The right end of 
the L.P. cylinder is receiving steam through port C from the left 
end of the H.P. cylinder. The L.P. cylinder is exhausting at D. 

The middle part of the valve is a simple piston valve for the 
L.P. cylinder. The two end portions constitute the valve for the 
H.P. cylinder. Both valves admit steam past their ends and ex- 
haust at the middle. 

OTHER FORMS. Valves of the pressure-plate type can be 
devised to take steam from the middle and to exhaust at the ends, 
but in this case the pressure-plate must be rigidly fastened to^ 
the cylinder, thus preventing relief from water. 

In many cases piston valves can be made similar to the- 
flat valves which have been described. 

There are many other forms of valves, but they are mostly^ 
modifications of those already described. 



CHAPTER III. 

SHAFT GOVERNORS. 

57. GENERAL*. The shaft governor is so called because 
it is mounted on the main shaft of the engine, being placed either 
ID the fly-wheel or in a governor case. It is a device which auto- 
matically regulates the cut-off so that the engine will supply just 
enough power to meet the demand, and, at the same time, main-' 
tain a nearly constant rotative speed for all loads within the 
capacity of the engine. As it works automatically, engines hav- 
ing such governors are frequently called "automatic engines." 

In general, a shaft governor has one, or two, pivotted 
' weight-arms," the centrifugal force acting on which is balanced 
by one, or more, springs which are so adjusted that there is a 
different speed and a corresponding definite and distinct position 
of the arm, or arms, for each different load on the engine. The 
"weight arms" are connected either directly, or by links, to the 
eccentric, so that for each speed there is a definite and distinct 
position of the eccentric, a corresponding cut-off, and a definite 
amount of power developed. If the load changes, the speed of 
the engine will also change until a cutoff is found which gives 
the right amount of power to balance the load. 

All so-called "constant-speed" governors are anomalies; for, 
while it is their function to maintain constant speeds — for them 
to act, it is necessary that a change in speed take place. How- 
ever, if the governor is of good design and properly adjusted, the 
amount of variation is very small (being from 1 to 2 i/^ % of the 
"normal" or average speed), so that the speed is practically con- 
stant. 

There are two general types of shaft governors — the "Centri- 
fugal" and the "Inertia." 



86 




58. CENTRIFUGAL GOVERNORS. The Sweet Governor, 
which was one of the earliest of this type, is shown in Fig. 68. 
Pivotted to one of the arms of the fly-wheel, or governor-wheel, 
is a "weight-arm," which has a heavy head W. When the en- 
gine is not running, this weight-arm is held in the "inner" posi- 
tion (that shown in full lines) by the leaf spring; and after 
steam is turned on, it will remain in this position until the speed 
has reached a certain point (for example, say 198 R.P.M.), when 
the centrifugal force C will just balance the spring pull. Now, 
if the speed is raised farther, the increased centrifugal force will 
cause the arm to move outward until, at some speed (say 202 
R.P.M.) it reaches the extreme "outer" position (that shown by 
the dotted lines). At the "normal" speed (2 00 R.P.M.) the 
weight-arm would be about midway between these extreme posi- 
tions; and for every other speed (between the 198 and 202 
R.P.M.) there are definite positions of the arm. 



In the example the total variation in speed is 2% of the 
normal R.P.M. By changing the adjustment of the spring, how- 
ever, the amount of variation can be changed, but if it is made too 
small, the friction and inertia of the valve gear, and the other 
disturbances, will make the action of the governor uncertain, so 
there is a practical limit to the closeness of regulation. 



87 



Again referring to Fig. 68, it is seen that the eccentric is 
pivotted at P to one of the arms of the wheel, and is connected 
by a link to an extension of the weight-arm. When this latter is 
in the inner position, or is "in," the center of the eccentric is at 
E., the position for the latest cut-off; and when it is "out," the 
eccentric-center is at e, the position for zero cut-off. 

The manner in which the governor operates is as follows: — 
Vv^hen the engine is standing still, the governor holds the eccen- 
tric in the position E for the latest cut-off. Then, if steam is 
turned on, the engine will speed up until a certain R.P.M. is 
leached at which the governor-arm will begin to move out, thus 
shifting the eccentric towards e and decreasing the cut-off. This 
movement continues until a position is reached at which the 
power developed just equals the load, and as long as this latter 
remains constant, the governor-arm will remain in this position. 
Now, if the load is reduced, the engine will speed up (tending to 
run-away) and this causes the weight-arm to fly out, shifting the 
eccentric towards e and reducing the power developed until it be- 
comes again equal to the load. Similarly, if the load is increased, 
the speed of the engine will decrease, and, as the weight-arm 
moves "in," the cut-off will be increased, until at some position of 
the arm a balance is again reached between the power and the 
load. 




Fig. 69. 

Fig 69 shows another "Centrifugal" Shaft Governor; but 
in this case there are two weight-arms, symmetrically placed, in- 
stead of one. In its action, this governor is identical with that 
which has just been described. 



88 



In both Figs. 68 and 69, it. is seen that the eccentric has a 
hole in its central web, made large enough to clear the shaft as 
the eccentric swings from one extreme to the other. In both 
cases the pivot is placed on the same side of the shaft as the 
crank pin. It is possible, however, to arrange the governor to 
nave a pivot on the opposite side, but this does not give as good 
a path for the center of the eccentric as does the former ar- 
rangement. The direction of rotation is such that the weight- 
arms trail behind their fulcrum-pins or pivots. 




59. INERTIA GOVERNORS. — Fig. 70 shows the Rites In- 
i-irtia Governor, which consists of a long weight-arm (WW), an 
eccentric pin E, and a spring. The arm is pivotted at P, close to 
the shaft, and its end W is heavier than W, so the center of 
gravitj- is at G. The position of the parts shown in full lines is 
lor -latest cut-off, and is the one occupied when the engine is 
not running; that shown by the broken lines, is for the earliest 
<?ut-off. In the former position, the arm is said to be "in," and 
in the latt'-^r, "out." The direction of rotation is shown by the 
^•^irrow. 

As the engine starts up, the governor-arm remains in the in- 
ner position until a certain speed is reached, when the centrifugal 
force 0, acting on the weight-arm, becomes great enough to bal- 



89 

ance the spring pull. Then, with a further increase in speed, the 
weight arm will move out, (the eccentric meanwhile moving 
toward e) until a sufficiently early cut-off is obtained. 

Now, if the load falls off, the engine will speed up, and the 
increased centrifugal force will cause the weight-arm to move 
out until the cut-off is reduced to the proper amount, the action 
being just the same as in the case of the Centrifugal Governor. 
However, in addition to the centrifugal force acting on the arm, 
there is also an inertia force which assists the movement. 

The inertia acts in this manner: — As the engine speeds up, 
the governor-arm tends to continue to rotate at its old speed, be- 
cause of its inertia, and hence lags behind the wheel, moving 
with respect to the lattar in the directon shown by the arrows 
l-I in the figure. It is seen that this movement is in the same di- 
rection as that caused by the centrifugal force. Again, if the 
load is suddenly increased, the engine will slow down, but, be- 
cause of its inertia, the weight-arm will continue at its old speed, 
thus gaining on the fly-wheel, and again assisting the centrifugal 
force in causing the motion. 

It is seen that the Inertia Governor is primarily a Centrifugal 
Governor, but that, in addition, the weight-arm is so pivotted, and 
has its weight so distributed that its inertia helps to cause the 
adjustment to take place, and that the more sudden the change 
in the load, the greater will be the assistance rendered. 

The eccentric or eccentric-pin is usually mounted directly on 
the weight-arm, or, in the case of the eccentric, is keyed directly 
to the end of the fulcrum pin opposite to that to which the arm 
is fastened. With these arrangements, in order to have the in- 
ertia of the weight-arm act in the right direction, the fulcrum pin 
must be placed on the side of the shaft opposite to the crank pin, 
when an external valve is used; and on the same side, when the 
Talve is internal. 

On center-crank engines the governor is frequently placed 
in the outer side of the wheel, in which case, since the shaft does 
not extend beyond the governor wheel, the arrangement can be 
that shown in Fig. 70. If, however, the governor is placed on 
the side of the wheel next to the engine frame, both the governor- 
arm and the eccentric must be made to surround the shaft In 
the manner shown at (a) Fig. 70. 



90 

60. SUMMARY. For both forms of shaft governors, it has 
been seen: — 

(a) That there is a definite speed, cut-off, and power for 
each position of the weight-arm. 

(b) That when the arm is "in," the speed is the lowest and 
the cut-off is the latest; whereas, if the weight-arm is "out," the 
reverse is the case. 

(c) That an increase in load decreases the speed and causes 
the arm to move "in," which gives a later cut-off; whereas, the 
effect of a decrease in load is the reverse. 

(d) That for close regulation, the friction and inertia of 
the valve-gear parts must be small, and especially is this neces- 
sary when the inertia form of governor is used. 

(e) In addition, in the case of the Inertia Governor, the 
fulcrum-pin must be placed opposite to the crank-pin if the ec- 
centric is attached directly to the governor-arm (or to its ful- 
crum-pin), and if an external valve is used. 

There are almost an unlimited number of forms of shaft 
governors, but all of them are merely modifications of those which 
have been described. 



CHAPTER IV. 

GEARS WITH SINGLE VALVE AND VARIABLE ECCENTRIC. 

6 1 . GENERAL. In the chapter on shaft governors, it was seen that 
in the process of regulating the engine, the governor changes the position 
of the eccentric with respect to the crank, varying both the throw and the 
angle of advance. How these changes affect the action of the valve will 
now be investigated. 




Fi©7t 



Fig. 71 is a "Diagram of Positions," showing the relative locations of 
the crank and the eccentric. The line SS^ is the ' ' steam lap line, ' ' its dist- 
ance from the Y-axis being equal to the steam lap. First suppose the angle 
of advance and the throw of the eccentric are respectively a^ and r^. Then, 
when the crank is on the dead center P, the eccentric will be at B^ If now, 
the eccentric is rotated back to a^, on SS^, it will be in the position for ad- 
mission. The corresponding position of the crank is A^. Starting from 
this phase and rotating the mechanism in the direction shown by the arrow, 
the valve will be open until the eccentric reaches c,, when cutoff will occur. 
The crank position for cutoff is C3 and it will be noticed that this event 
comes quite late in the stroke. The maximum opening of the valve is 
shown by the distance 1-3 ; the lead opening is equal to the distance that 
E3 is to the right of the line SS^, and the lead angle is g>y 

Next, suppose that the eccentric is moved to a new position with respect 
to the crank, so that it will be at Bj, when the crank pin is at P, the new 
angle of advance a^ being greater than that in the previous case, and the 
throw r, being less. It will of course be found that this shifting of the 



92 

eccentric has changed the action of the valve. As the mechanism rotates 
in the direction of the arrow, admission takes place when the eccentric and 
crank are respectfully at a^ and Ag ; and cutoff occurs with these at c, and 
Cj. It is seen that cutoff is now much earlier than it was in the previous 
case and it is evident that this change was brought about by increasing the 
angle of advance. The maximum opening is now given by the distance 1-2, 
which is less than that in the previous case, as would be expected with the 
decreased throw. The lead is the distance between B2 and SS^. 

Again, suppose the eccentric is moved to a position Bi, just opposite the 
the crank P (the angle of advance being 90 deg. ) with the throw just equal 
to the steam lap. Then the valve will not open at all but when the crank 
is on dead center it will have its maximum displacement and its edge will 
be just even with the port edge. Nominally the cutoff, the lead, the lead 
angle and the maximum opening are all zero. 

From the forgoing it is evident that the cutoff and the lead angle ( or 
lead) can be changed in any way that is desired by merely shifting the 
eccentric to the proper position with respect to the crank, and that the 
shifting also affects the width of valve opening. Later it will be seen that 
this also changes the exhaust events. 

In Fig. 76 are shown theoretical indicator cards for several different cut- 
offs, and it is seen that when the cutoff is made to occur earlier, the release 
and compression also take place sooner. 

The shaft governor, which controls the positions of the eccentric, should 
be so arranged that as the weight arms move ' ' out, ' ' as they do when the 
load is decreased, the eccentric will be shifted "in " (toward EJ to give an 
earlier cutoff, and vice versa. 

62. THE BILGRAM DIAGRAM. 




In Fig. 72 is shown the eccentric-path K3E1, the crank being on the dead 
center P. When the eccentric is at B3, the throw is OB3 and the angle of 
advance a^. On the Bilgram diagram, Fig. 73, the position of the lap cir- 
cle center Q^, corresponding to E3, is found in the usual manner, by draw- 
ing OQ3 at the angle a^ with the X-axis and making OQ, equal to OE^. The 
action of the head end of the valve, for this particular throw and angle of 
advance of the eccentric, may be studied by drawing the steam and ex- 



93 



haust lap circles with Q^ as center, just as in the case of the ordinary gear 
with the fixed eccentric. The lap circles for the crank end would have cen- 
ter at q^, diametrically opposite Q3. 

If the eccentric is now moved to a new position E2, Fig. 72, it has a new 
throw and a new angle of advance. Laying these off on the Bilgram Dia- 
gram, Fig. 73, the new lap circle center Qj is located, and with this as cen- 
ter the lap circles may again be drawn and the action of the valve deter- 
mined for this case. 

The positions of Q, corresponding to the other positions of E, may be 
found in a similar manner. The curve through these points will be termed 
"the path of the lap circle center," or more briefly '' the lap-circle path." 

If Fig. 72 is superimposed on Fig. 73, as in Fig. 74, it is apparant that 
the paths of Q, and E are symmetrical with respect to the 45 deg*. 
line bisecting the quadrant XOY. It is also evident that, in Fig. 73, 
the paths of Q and of q are symmetrical with respect to O. 

The shifting of the eccentric of course in no way changes the proportions 
of the valve, so for all positions of Q the lap circles would be the same. 

Fig. 75 is a Bilgram Dia- 
gram for the head end of 
the valve, for three positions 
of Q. It shows that, as 
the eccentric is moved 
"in" (i.e. as the lap- 
circle center is moved to- 
wards 0,1 ), all the events 
are made to occur earlier 
in the stroke, (with the 
possible exception of admis- 
sion, ) and that the maxi- 
mum opening w is de- 
creased. 

It further shows that the 
lead is decreased in this 
particular case. In general, 
however, the way the lead 
and lead angle (admission) 
vary depends on the charac- 
ter of the path of Q (and of 
B) ; and this to a certain 
extent, also has an influence 
on the widths of valve open- 
ing. So in designing, the 
character of the lap-circle 
path must carefully be con- 
sidered. 




94 

In Fig. 76 are shown theoretical indicator cards corresponding to two 
positions of Q shown in Fig. 75, and also for two other positions of this point, 
which are omitted from the former figure to avoid confusion. These cards 
show clearly how the release and compression vary with the cutoff. 

Suppose it is desired to design a valve gear of this type, and that 
latest cutoff is to occur when the crank is at C^, in Fig. 75, with w^ as the 
maximum opening of the valve, and 1^ the lead. On the Bilgram Diagram, 
just as for an ordinary slide valve, there would be drawn the lead line 1, 
the arc with radius equal to the desired maximum opening w^, and the 
crank position OC^ for C. O. ; then Q^ would be so located that the lap 
circle would be tangent to all three of these lines, thus determining the 
steam lap, the throw and the angle of advance. Then assuming one of the 
exhaust events, the size of the exhaust lap would be fixed and the propor- 
tions of the valve and eccentric would be determined. 

It is next necessary to decide on the character of the path of Q (and of B). 
In this case, this path is an arc of a circle drawn in such a way that when 
the lap circle center is at Q^ the lead and cutoff are zero. 

Having drawn the path of Q, suppose it is desired to study the action of 
the valve when the cutoff occurs with the crank at some position, say C3. 
To determine the location of the lap circle center, we know that it must be 
on the path of Q, and that the circle itself must be tangent to OC3 ; thus its 
position is definitely fixed. The Bilgram Diagram for this position can 
then be completed, and the action of the valve be studied. 

In determining the size of the exhaust lap it is necessary to consider 
both the minimum and the maximum amounts of compression that are ob- 
tained. When the cutoff is that for friction load it is desirable that the 
pressure at the end of compression should not be above boiler pressure ; 
for if it exceeds this, the valve will clatter, if of the lifting type, and if 
not of this type an undesirable excess in pressure results. On the other 
hand, when the cutoff is latest, the compression is least and it should then 
be great enough to properly cushion the reciprocating parts. The range 
of compression should be kept within these limits if possible. 

63. ELLIPTICAL DIAGRAM. Fig. 
77. For each position of the eccentric in its 
path, there will be a separate ellipse, which 
can be obtained in the usual way. The dia- 
gram shows clearly how the shifting of 
the eccentric effects the valve - openings 
and events. The relative sharpness of these 
latter is indicated by the slope of the ellipses 
where they cross the lap lines. Thru the 
maximum points M there has been drawn 
a curve ( ' ' the locus of M " ) which will be referred to later. * 




95 





\j&^^Z 


Y 






rtVS^- ^ 


1 

1 




A : 

M 


V^ 


1 


m) 




^i"""^^-— _ 




;:^^>^.*7d 




5 








F.*73 



64. ZEUNER AND SWEET DIAGRAMS. These are shown re- 
spectively in Figs. 78 and 79, and are constructed in|the usual manner, tak- 
ing each position of the eccentric in turn. It is'seen that the loci of M and 
of E are symmetrical with respect to the Y-axis. 

66. BARR DIAGRAM. In Fig. 80 
(a) shows the path of a swinging eccen- 
tric when the crank is at P, and (b) is 
the corresponding Bilgram Diagram. 
For each of the three positions of B 
and Q shown, the crank-position M for 
maximum opening has been found, by 
drawing it at right angles to OQ. The 
corresponding positions of the piston 
are i, 2 and 3. 

If the piston is assumed to have sim- 
ple harmonic motion, its velocity, V, is 
proportional to the sine of the crank 
angle, or, what is the same thing, to the 
ordinate of the crank pin. Referring to 
equation 3 on page 42, it is seen that, 
for a given velocity of steam (v) and 
ceilain area of piston (A), the valve 
opening (a) should be proportional to 
the velocity of the piston ( V ) , which we 
have just seen is a function of the ordi- 
nate of the crank pin. Therefore, in 
drawing a curve of desired openings, its ordinates would be made directly 
proportional to those of the crank pin. This curve, a-b-c in Fig. 80 (c), is 
of course an ellipse, which can be readily constructed as soon as one point 
has been determined. 

Now suppose the desired width of opening for the latest cutoff 
(ecc. at B3 in its path) has been found to be W3. This maximum opening 







% 

occurs when the piston is at 3, at which point, in Fig. 80(c), w^ would be 
erected as an ordinate, thus giving one point (c) on the curve. Through 
(c) the curve of desired maximum opening's can then be drawn by con- 
structing the elliptic arc a-b-c. Now, if the eccentric is moved to position 
Ea in its path, the maximum opening then occurs when the piston is at 2, 
and from the curve just drawn it is seen that the width of opening 
should be equal to the distance 2-b, in order to have the same velocity of 
steam as before ; and similarly for other positions of the eccentric in 
its path. 

Going back to the Bilgram Diagram, Fig. 80 (b), and drawing the steam 
lap circles, the actual maximum openings, Wj, Wj and W3 are found. In 
Fig. 80 (d) these are shown plotted on their respective piston positions, 
giving the curve d-e-f, (which is seen to be the same as the locus of M in 
Fig. 77, when referred to the steam-lap line as a base. ) 

The curves of desired and actual, maximum openings should of course be 
identical, but in Fig. 80 (e) where they are both plotted on the same base, 
it is seen that the actual openings are smaller than the desired, except 
at the extremes. This reveals one of the faults of this type of gear, but it 
can be partly remedied in several ways. 

One of the ways of increasing the maximum openings, for the inter- 
mediate cutoffs, is to give the path Q greater curvature in an upward 
direction ; for in Fig. 80 (b) it is seen that if Qj is raised, the opening w, 
will be correspondingly increased. Another way is to increase the size and 
travel of the valve, the valve diagram remaining the same, except as to 
scale ; but as this gives openings which are larger than are needed for later 
cutoffs, and especially as it involves increasing the size of the valve-gear 
parts, it is an undesirable method. A better way is to make the valve mul- 
tiported, thus obtaining even larger openings than in this last case, without 
changing the eccentric. The maximum openings for a double-ported valve 
are shown by curve 6 in Fig. 81, in which 5 gives the openings for a single- 
ported valve and 7 those that are desired. It is seen, however, that for the 
later cutoffs the openings are still wider than are needed. But if the valve 
has an auxiliary port like that in the Sweet type of valve, the wider open- 
ings can be made to approximate quite closely those that are desired. The 
way this can be done will now we considered. 



97 




FieSl 



Let the positions of the Sweet Valve 
shown in Fig. 82, be the extreme ones cor~ 
responding to different locations of the 
eccentric in its path. Then the respective 
phases of maximuni opening' are seen to 
be the following : — ( 1 ) Double-ported, so 
long as the maximum displacement of the 
valve is such that the opening y, in Fig. 82a, 
is less than the width of the auxiliary port 
(a). (2) Sing-le- ported plus a constant, 
(Fig. 82b), when the throw is greater than 
this amount, the constant quantity being 
equal to (a). (3). Constant (Fig. 82c) 
when auxiliary port is partly closed by the 
exhaust edge of the valve seat, the opening 
k being equal to (W-B). And (4) Single- 
ported (Fig. 82d) when the auxiliary port is entirely closed when the valve 
is in the extreme position. 

In Fig. 81 the maximum openings, for the different 

positions of the eccentric in its path, are shown by 

the heavy line 1-2-3-4, the parts being numbered to 

jl» OUj correspond with the phases just described. The first 

■W\ ^^k Q phase ends when the ordinate is equal to 2 a and the 

^^ ' ^^r^ second? terminates when the ordinate equals k, which 

in turn is equal to (W-B). 

In proportioning- a Sweet Valve for this type of 
gear, the curve of desired maximum openings ( 7 ) and 
^^- that of the actual openings ( 5 ) for a single ported 

^^^ Q valve, would be drawn first. By doubling the ordi- 
^^ nates of 5 the curve i for the double ported phase 

would be obtained. Then assuming a suitable width 
of the auxiliary port (a) curve 2 for the second 
phase can be obtained by adding the constant quan- 
tity (a) to the ordinates of 5. The height (k) of the 
line 3 for the third phase can be so drawn as to 
make the curve approach 7 as close as possible. Then 

assuming the width B of the bridge-end of the valve, 

I ^^■■■i the width of port W in the valve seat is fixed (since 
^^^ m^mgJL \V = k -f B ) and this must of course be at least as 
^^m*^^9^ fX large as the width of the cylinder passage. The valve 
^^ *^ and valve seat can then be drawn, using the values of 
Fig. 82. a, B and W which have been determined. If the valve 

is made quadruple ported, as in the case of the Wood- 
bury (§52), a still closer approximation to the desired openings can be ob- 
tained, but this is at the expense of greater complication. 

The above method of determining the proportions of the Sweet Valve is 
due to Professor J. H. Barr. 






98 




Fi6 83 

Fig. 83 shows a Diagram of Opening's, whicli is that part of the Ellipti- 
cal Diagram which lies above the steam lap line. This has been corrected 
to show the effect of the auxiliary port in the valve. The diagram for the 
greatest travel is similar to that shown in Fig. 56 and shows all four phases 
of opening and closing. The intermediate curve shows only two phases, 
and the smaller one, one phase. This diagram has been drawn very much 
distorted for the sake of clearness. If it is drawn accurately it will be 
found that on it the locus of M is the same curve as 1-2-3-4 in Fig. 81. 

On the Zeuner and the Sweet diagrams in Figs. 78 and 79, the eifect 
of the auxiliary port can also be shown, as it is in Figs. 57 and 58, for 
the greatest travel. 

66. THE PATH OF THE ECCENTRIC. In selecting this, one 
must consider not only the manner in which the eccentric is to be moved 
by the governor, but also how the character of the path influences the 
action of the valve. 

In general there are two different ways in which the eccentric is moved. 
In the first, it is shifted over a straight-line path, and is called a "shifting 
eccentric." In the second it is swung about a pivot, and is therefore 
called a " swinging eccentric." This latter, arrangements of which are 
shown in Figs. 68, 69 and 70, is the one more commonly adopted as it usually 
involves less complication in the governing mechanism than does the former. 

The character of the path of the eccentric has an important influence on 
the steam distribution, as it affects the lead angle, the exhaust events, and 
the valve opening. 

First we will consider the " shifting eccentric", taking up two general 
cases. 

Case I. Constant Lead-Opening. In Fig. 84 at (a) is shown the ec- 
centric-path, which is parallel to the Y-axis, and gives constant lead. It is 
seen in the corresponding Bilgram Diagram, (b) in this same figure, that as 
Q is shifted to the left, the admission. A, is made to occur earlier ; that altho 
the lead opening remains constant as shown by the line 1, the lead angle (p 
varies greatly, which ordinarily is undesirable. 

Further it is evident that it is not possible to obtain a cutoff at zero stroke, 
for no matter how far Q is shifted to the left, the crank position OC for cut- 
off can never become horizontal. However, it is not usually necessary to 



99 



provide for as early a cutoff as this, since there is always the friction of the 
engine to be overcome. Further, the very early admission assists the cut- 
off in reducing the area of the indicator card. 

Ordinarily the position of the eccentric below Kq in Fig. 84a, would be 
that for rotation in the opposite direction ; but in this case where the lead- 
opening is large, if the engine is once started, the direction will not be re- 
versed, until B is shifted below the point Bi some little distance. 




FiG&5^ 



Case II. Constant Lead-Angle. In Fig. 85a it is seen that as the 
eccentric is shifted " in " the lead is decreased uniformly, becoming zero 
when Bi is reached. The Bilgram Diagram shows that the crank position 
A for admission remains the same for all positions of Q, the lead-angle being 
constant. It is also seen that zero cutoff can be obtained. Ordinarily 
these are desirable attributes. 

In both Figs. 84 and 85 the maximum width of valve opening is the same 
when the lap circle center is at Q3. But, when Q is in the other positions, 
it is seen that in Fig. 84 there are wider openings than in Fig. 85, and Case 
I would therefore be the one selected if there was nothing else to be con- 
sidered beside the openings. 

In Fig. 86, in which are shown both cases, OC is the crank position for 
the normal cutoff ( say at %. stroke ) . QI and QII are the respective lap cir- 
cle centers for the two cases, and are of course at a distance from OC equal 
to the steam-lap. For convenience suppose the exhaust lap circles are of 
zero radius. It is seen that both release and compression occur later in 
Case II than in Case I, and as these events usually come earlier than is de- 
sired, Case II would be selected if there were no other considerations 
involved. 

In the case of the swinging-eccentric, the path, which does not usually 
have very great curvature, may be considered as approximating the straight 
line path of the shifting eccentric, so that all that has been said in regard 
to this latter also holds for the swinging eccentric with_^slight modification 
which will now be considered. 



100 




Case A. In Fig. 87, (a) shows an arrangement of the swinging eccentric 
like that shown in Fig. 68, the pivot for the eccentric being located at p, 
on the same side of the shaft as the crank pin. In the Bilgram Diagram A 
is the corresponding path of Q, 

Case B. In Fig. 87, (b) shows an arrangement like that ordinarily used 
in connection with the inertia type of governor illustrated in Fig. 70, the 
eccentric-pivot, p, being placed opposite the crank. On the Bilgram 
Diagram, B is the corresponding path of Q. 

Comparing the last two cases with each other, it is seen that Case A gives 
the greater openings, while the exhaust events occur later in Case B. It is 
also seen that the straight line path of Q (I in Fig. 87) gives openings and 
exhaust events intermediate between these two cases. ' 

From the foregoing discussion, it is evident that the selection of the 
eccentric path is a matter of compromise. As to which kind of path is 
the best, opinions differ, and no general rule can be given. One must 
decide what things are most important for the particular case at hand, and 
favor those as much as is allowable. In selecting the path the following 
general rule will be of assistance : — For any given cutoff, a change in the 
path involving the raising of Q, will increase the valve-opening, the lead, 
the lead angle, the release and the compression ; whereas a change in the 
reverse, direction will of course have the opposite effect. 

Since the admission and the compression are, in a way, complimentary 
to each other, the admission can occur quite late, when the cutoff is very- 
early, since in this case the compression pressure is very high. Some de- 
signers even use negative lead for the very early cutoffs. 

It is of course desirable to be able to use the same governor wheel and 
parts, no matter which way the engine runs, and in selecting the path this 
should be kept in mind. When the governor is of the Rites inertia type, 
the eccentric pivot is usually placed on the center line of the crank for this 
reason. 



101 

67. EaUALIZATION OF EVENTS. For any one position of the 
eccentric in its path, the events can of course be equalized in the ways that 
were explained for the simple gear with fixed eccentric (§§ 22-24). Equal- 
ization for all positions of the eccentric in its path is impossible, but can be 
approximated more or less closely, by methods which will now be explained. 




Fig 66 



(a) Equalization of Admission. Supposing that it is desired to have 
constant and equal admission at all times in the two strokes, let A and a in 
Fig. 88 be the respective desired crank positions for these events and let A/ 
and a'' be the corresponding positions of the eccentric-path. Let BGb be 
the position of the rocker for admission at the head end, at which time the 
edge of the valve is of course even with that of the port ; and let DGd be 
the corresponding rocker position for the crank end. 

To have admission at the head end occur only when the crank is at A it 
is evident that all points on the path A'' must be at a distance from B equal 
to the length of the eccentric rod, or in other words, that an arc L^, struck 
with B as center and with a radius equal to the length of the eccentric rod 
must coincide with A'. Or, given the path A'', it is of course possible to 
find a position of B which will give coincidence between these arcs. 

To have constant admission at the crank end the point D should be so 
located that the eccentric-rod arc V (struck with D as center) will coincide 
with the path a', but this is not possible. Hence while constant admission 
can be obtained at one end of the cylinder, it can not be at the other. 
Since it is not possible to have the admission vary the same way at both 
ends, equalization of this event for all positions of the eccentric in its path 
is not possible in this case. 

In general exact equalization of admission is obtainable only when the 
path of the eccentric is a straight line and the eccentric rod is of infinite 
length, so that, in practice exact equalization is never obtainable. However, 
it can be approached more or less closely by using as small a curvature for 
the eccentric path, and as long an eccentric rod, as the other considerations 
will permit. 

Since an oblique guide is used, the valve motion is not harmonic, and 
hence the valve diagrams can be used only to get the throws and angles of 



102 



advance of the eccentric together with the crank positions for the events. 
The actual laps and openings can be obtained only after the positions of the 
rocker (or oblique guide) have been found as in Fig. 88. In this figure 
FGf is the central position of the rocker, UGu is its extreme position to 
the right and VGv that to the left. The steam lap for the head end is given 
nominally by the horizontal projection of the distance fb, while that for the 
crank end is the projection of fd. The projections of bu and dv give the 
corresponding maximum openings. 




Fis69 



(b) Equalization of Lead. In Fig. 89, when the crank is on the head 
end dead center P ( at which time the valve is open to lead) let E be one 
position of the eccentric in its path B'', and let B^Gb'' be the corresponding 
position of the rocker. As before, BGb is the rocker position for admission, 
and Iv'' is the eccentric-rod arc struck with B as center. 

The lead opening, which is equal to the horizontal projection of bb'', can 
be produced by moving the eccentric through the horizontal distance LB, 
and it is evident that, no matter where the eccentric is in its path B^, its 
horizontal distance from the arc Lt^ is a measure of the lead, (but not neces- 
sarily equal to it >. 

Evidently the amount of lead, and the way it varies, can be controlled 
largely by the position selected for B. In designing, then, we would locate 
B, the position of the eccentric in its path for normal load, and lay oif the 
distance I^B to represent the lead ; then we would so locate B that the dis- 
tance between the arcs Iv^ and E'' varies in the way we wish the lead to 
change, as the eccentric is shifted over its path. 

Similarly for the crank end, e^ is the path of the eccentric when the crank 
is on the dead center P^ ; e is the position of the eccentric corresponding to 
B ; D^Gd'' is the rocker position for lead and DGd that for admission ; V is 
the eccentric-rod arc struck with D as center ; and the distance el is a meas- 
ure of the lead for this position of the eccentric. It is desired to so locate 
D that, as the eccentric is shifted, the distance between V and e^ will vary 
in the same way as that between h^ and E^, but it is evident that this is im- 



103 

possible, so equalization of lead for all positions of the eccentric in its path 
is not possible in this case. As before, the desired result can be obtained 
only when the eccentric path is a straight line and the eccentric rod is of 
infinite length. 




riG.'So 



(c) Equalization of Cutoifs. Having first obtained from a Bilgram 
diagram the throws and angles of advance of the eccentric for the different 
cutoffs, a diagram like Fig. 90a may be constructed to show the desired 
positions of the piston, crank and eccentric for the various cutoffs. In this 
figure, let 2 be the position of the piston for cutoff in the forward stroke and 
2^ be that for the return and let O — 2=0 — 2^. Then by drawing the con- 
necting-rod arcs, the corresponding crank-pin positions C, and c^ are found. 
Next, using the throw and angle of advance of the eccentric (obtained from 
the Bilgram Diagram ) for this particular cutoff, the corresponding positions 
of the eccentric can be found. Supposing the valve takes steam from the 
middle, in which case the eccentric follows the crank at an angle equal to 
(90 deg.— angle of advance), the eccentric positions are found to be B2 and 

Again, if it is desired to have cutoff occur when the piston is in positions 
I and I'' respectively, the corresponding locations of the eccentric will be 
found in a similar manner to be at Ei and e^. 

If the cutoff is at zero stroke, the eccentric positions at the time of this 
event are Eq and e^. 

The lines S and s through the two sets of points (E and e) thus obtained 
are the loci of the desired positions of the eccentric at the times of cutoff at 
the two ends of the cylinder. 

In Fig. 90b, in which the loci S and s are again drawn, B is the position 
of the rocker pin for cutoff at the head end, at which time the edge of the 
valve is even with the port edge, and D is the position of the pin for crank- 
end cutoff. Then, to have the cutoff occur as desired, it is evident that all 



104 

points in S should be at a distance from B equal to the length of the eccen- 
tric rod, and that points in s should be at the same distance from D. Evi- 
dently equalization throughout the whole range can not be obtained. The 
best that can be done is to so locate B and D that the eccentric- rod arcs h^ 
and V will coincide respectively with S and s as nearly as they can be made 
to, but in any case these arcs should pass through the positions of the eccen- 
tric for normal cutoff, so that this event will at least be equalized when the 
engine is operating under normal conditions. 

The foregoing method applies equally as well to the case of the direct 
driven external valve, as to that of the internal valve. 

(d) Equalization of both the Cutoflfs and the Admissions. This 
can be approximated only when the eccentric follows the crank, as it does 
when either the direct-driven internal valve, or else the external valve with 
reversing rocker, is used. Referring to Fig. 90b, A^ and a^ are the respec- 
tive positions of the path of the eccentric for equal lead-angles at the two 
ends of the cylinder, the crank positions being A and a. As before, B is the 
position of the rocker pin when the edge of the valve at the head end is 
even with the edge of the port, which is the position both for cutoff and for 
admission, depending on the direction of the motion of the valve. D is the 
position of this pin for the corresponding crank end events. To have both 
the admission and the cutoff equalized, B must be so located that the 
eccentric rod arc h^ will coincide with both A'' and S ; and D must be so 
placed that V will coincide with a^ and s. Equalization throughout the 
whole range is of course impossible, but it can be approximated, and exact 
equalization for one point of the eccentric in its path, say that for normal 
load, can be obtained. 

(e) Equalization of Exhaust Events. Having equalized as nearly as 
is possible the steam events, one of the exhaust events may be equalized 
for one particular position of the eccentric in its path, by using unequal 
exhaust laps, which may be found in the way that was described in § 24. 

( f ) General. Because the valve motion is distorted when an oblique 
rocker is used, the valve diagrams can be used only to get the throws and 
angles of advance of the eccentric and the crank positions for the events. 
On them the laps and openings are merely nominal ; the actual values of 
these can only be obtained after the positions of the valve-rod pin on the 
rocker has been found, which can be done in the manner that was explained 
at the end of § 67a. 

If the eccentric leads the crank, it is found that the valve openings at 
the crank end are larger than those at the head. Preferably, however, the 
head end openings should be the larger, for the velocity of the piston is 
greater near that end of the stroke than when near the crank end (because 
of the "angularity" of the connecting rod). If the eccentric is placed 
behind the crank, in the position it occupies when the valve is internal, or 
when a reversing rocker is used with an external valve, the larger openings 
will come at the head end as they should. 



105 

Instead of using a bell crank as a guide, there may be substituted an 
oblique crosshead like that in Fig. 34a, or a simple oblique rocker, with 
eccentric and valve-rod pins co-axial. 

As first laid out, it may be found that the valve openings actually ob- 
tained are not satisfactory. These openings can of course be remedied by 
changing the throw of the eccentric, but if a bell crank is used the ratio 
between the two arms can be altered so as to produce the desired result. If 
this change necessitates having the eccentric rod oblique to the center line 
of the engine, the eccentric path must be shifted to correspond. 

68. SUMMARY. In designing a valve gear of this type the following 
steps would be taken : — 

(a) Having determined the maximum valve opening and having assumed 
the lead, construct a Bilgram Diagram for the latest C. O. (say % or ^ 
stroke). 

(b) Assume a path of the eccentric (or of Q) to suit the arrangement of 
the governor and to give the best steam distribution obtainable (§ 66). 

(c) Determine the size of the exhaust laps (§62) first so that when the 
cutoff is the latest there will be sufficient compression to cushion the 
reciprocating parts ; second, so that when the cutoff is that for friction load, 
the pressure at the end of compression will not exceed that of the steam ; 
then use the smaller of the two laps obtained. If it is desired to equalize 
the exhaust events this may be done for one position of the eccentric in its 
path, say that for normal load, by using unequal laps which may be found 
in the manner given in § 22. 

(d) To show more clearly the action of the valves than is done by the 
Bilgram Diagram, the Elliptical Diagram may be drawn (§63). If desired, 
the Zeuner and Sweet Diagrams can also be constructed at this stage (§ 64), 

(e) The other proportions of the valve, which is assumed to be of the 
Sweet type, may then be determined by constructing the Barr Diagram of 
Maximum Openings as in § 65. 

(f ) If it is desired to attempt the equalization of the events, this can be 
done by the "cut and try " methods outlined in § 67. 



.BMy'08 






THE DESIGN OF 



VALVE GEARS 



FOR 



STEAM ENGINES 



BY 



WILLIAM N. BARNARD 

Professor of Steam Engineering, Sibley College 
Cornell University 

Copyright 1907. 

fey W. H. 0AliKARD, 



-^ s^^c^'^-^^^r 



W'^^ff^y^ 



XiiHARY of CONGRESS 

\ww Ct'Dles Received 1 

oci 1 »90r 

Copynfht Entry 

CLASS/^ XXCm No. 

COPY d. 



